Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.展开更多
Radioactive nuclides as 131I and 133Xe are increasingly used for both clinical diagnosis and therapeutic treatment of the patient. For example, 131I is used for the treatment of thyroid gland cancer. Otherwise, 133Xe ...Radioactive nuclides as 131I and 133Xe are increasingly used for both clinical diagnosis and therapeutic treatment of the patient. For example, 131I is used for the treatment of thyroid gland cancer. Otherwise, 133Xe is used in ventilation studies to assess and evaluate pulmonary function and to provide images of the lungs in both cardiac and pulmonary diseases, such as asthma, pulmonary emphysema, bronchiectasis, carcinoma of the lung, and pulmonary embolism [1,2]. Furthermore, cerebral blood flow is measured using 133Xe inhalation. In this study, the X and γ-rays emission probabilities in the decay of 131I and 133Xe were precisely measured with a calibrated Si(Li) detector. Results of this study were compared using available results in the literature. Good agreement was observed between our results and available results in the literature.展开更多
With the development of ocean engineering, it is one of the most important factors which determine the structural safety, cost and suitable forms of engineerings to select the ocean environmental design criteria. Owin...With the development of ocean engineering, it is one of the most important factors which determine the structural safety, cost and suitable forms of engineerings to select the ocean environmental design criteria. Owing to the complexity , variation and randomness of ocean environmental conditions, the commonly used methods for determining design criteria cannot consider the joint occurring probabilities of several environmental factors ,therefore, lead to overestimate design criteria of them and result in an unnecessary overspend invest in engineering. On the basis of the measured and hindcasting data and the multi-demension joint probability theory, this paper presented the study of the joint loads of wind , wave and current on the offshore structures and its responsible joint probability level with the application of random simulation techniques, and presented the joint design criteria of environmental loads for the realistic design of engineerings.展开更多
The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss...The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.展开更多
Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the rob...Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.展开更多
Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to...Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to negatively skewed ones,and their means are concave-down functions of time.When payments are set to zero or proportional to the firm value,EMM turns into the Geometric Brownian model(GBM).We show that risk-neutral probabilities(RNPs)and the no-arbitraging principle(NAP)follow from GBM.When firm’s payments are considered,RNPs and NAP hold for the entire market for short times only,but for long-term investments,RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant,and fail when the mean year returns decline.The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.展开更多
In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting ...In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.展开更多
A SEI model for hepatitis B is constructed where the susceptibility and other crucial transmission probabilities depend on the chronological age and the basic reproduction rate R0 is derived. Under suitable (biologica...A SEI model for hepatitis B is constructed where the susceptibility and other crucial transmission probabilities depend on the chronological age and the basic reproduction rate R0 is derived. Under suitable (biological and mathematical) assumptions in a closed population, results of Houpa D. D. E. et al. [1] are extended from constant case of p and q to age-dependent case: the disease-free equilibrium is globally asymptotically stable (GAS) if R0 . On the other hand, R0 > 1 induces that endemic equilibrium is GAS and the system is uniformly persistent.展开更多
This paper outlines a two-stage assessment procedure for deriving probabilities of unique events.The calculations are illustrated using possible events pertaining to the Lehman failure in 2008.The procedures utilize p...This paper outlines a two-stage assessment procedure for deriving probabilities of unique events.The calculations are illustrated using possible events pertaining to the Lehman failure in 2008.The procedures utilize pairwise comparisons associated with the Analytic Hierarchy Process.Typical betting odds are used to motivate an ordering of qualitative judgments that are then converted into quantitative assessments and finally a probability distribution.展开更多
Decision-makers in unique or one-off situations may have difficulties in framing the probabilities of possible events that are required in modern decision-making. This paper illustrates a new approach to probability d...Decision-makers in unique or one-off situations may have difficulties in framing the probabilities of possible events that are required in modern decision-making. This paper illustrates a new approach to probability determination based on pairwise primary judgments on the relative likelihoods of the possible events. Related “news” on the situation can also be used to update these prior probabilities using Bayesian Revision. Illustrative calculations outline the entire process through to determination of posterior probabilities following a “news” event.展开更多
Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and com...Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.展开更多
In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain wit...In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.展开更多
Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relat...Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relativistic effects are considered. The calculations are compared with other results in the literature. A good agreement is found. We also report on some unpublished energy values.展开更多
The current AASHTO load and resistance factor design (LRFD) guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the...The current AASHTO load and resistance factor design (LRFD) guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads (also referred to as multiple hazard or MH loads) can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions: (1) formulate the failure probabilities; (2) normalize various load distributions; and (3) establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.展开更多
Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the Na...Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the National Institute of Standards and Technology. The transition probability for a line of 424.18nm is reported for the first time. Meanwhile, a feasible method of calculating transition parameters related to special excited configurations or highly excited states is provided.展开更多
We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors (financial risk...We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors (financial risk) {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278-1299).展开更多
Configuration evaluation is a key technology to be considered in the design of multiple aircrafts formation(MAF)configurations with high dynamic properties in engineering applications.This paper deduces the relationsh...Configuration evaluation is a key technology to be considered in the design of multiple aircrafts formation(MAF)configurations with high dynamic properties in engineering applications.This paper deduces the relationship between relative velocity,dynamic safety distance and dynamic adjacent distance of formation members,then divides the formation states into collision-state and matching-state.Meanwhile,probability models are constructed based on the binary normal distribution of relative distance and relative velocity.Moreover,configuration evaluation strategies are studied by quantitatively analyzing the denseness and the basic capabilities according to the MAF collision-state probability and the MAF matching-state probability,respectively.The scale of MAF is grouped into 5 levels,and previous lattice-type structures are extended into four degrees by taking the relative velocities into account to instruct the configuration design under complex task conditions.Finally,hardware-in-loop(HIL)simulation and outfield flight test results are presented to verify the feasibility of these evaluation strategies.展开更多
Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which ...Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.展开更多
Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are sel...Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.展开更多
On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broad...On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R,The theoretically predicted transition probabilities are in good agreement with the experimental ones.PACS numbers: 71.70.Ch, 78.20.Nv, 63.20.Mt, 63.20.展开更多
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
文摘Radioactive nuclides as 131I and 133Xe are increasingly used for both clinical diagnosis and therapeutic treatment of the patient. For example, 131I is used for the treatment of thyroid gland cancer. Otherwise, 133Xe is used in ventilation studies to assess and evaluate pulmonary function and to provide images of the lungs in both cardiac and pulmonary diseases, such as asthma, pulmonary emphysema, bronchiectasis, carcinoma of the lung, and pulmonary embolism [1,2]. Furthermore, cerebral blood flow is measured using 133Xe inhalation. In this study, the X and γ-rays emission probabilities in the decay of 131I and 133Xe were precisely measured with a calibrated Si(Li) detector. Results of this study were compared using available results in the literature. Good agreement was observed between our results and available results in the literature.
文摘With the development of ocean engineering, it is one of the most important factors which determine the structural safety, cost and suitable forms of engineerings to select the ocean environmental design criteria. Owing to the complexity , variation and randomness of ocean environmental conditions, the commonly used methods for determining design criteria cannot consider the joint occurring probabilities of several environmental factors ,therefore, lead to overestimate design criteria of them and result in an unnecessary overspend invest in engineering. On the basis of the measured and hindcasting data and the multi-demension joint probability theory, this paper presented the study of the joint loads of wind , wave and current on the offshore structures and its responsible joint probability level with the application of random simulation techniques, and presented the joint design criteria of environmental loads for the realistic design of engineerings.
文摘The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.
基金Supported by the National Natural Science Foundation of China(71571019).
文摘Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.
基金The author is infinitely thankful to his friend and colleague M.Rubinstein for valuable discussions and an invariable interest to his work.The author is also thankful to C.Miller for his high estimation of the author’s efforts.Of course,all errors are author’s full responsibility.
文摘Extensions of Merton’s model(EMM)considering the firm’s payments and generating new types of firm value distribution are suggested.In the open log-value/time space,these distributions evolve from initially normal to negatively skewed ones,and their means are concave-down functions of time.When payments are set to zero or proportional to the firm value,EMM turns into the Geometric Brownian model(GBM).We show that risk-neutral probabilities(RNPs)and the no-arbitraging principle(NAP)follow from GBM.When firm’s payments are considered,RNPs and NAP hold for the entire market for short times only,but for long-term investments,RNPs and NAP just temporarily hold for individual stocks as far as mean year returns of the firms issuing those stocks remain constant,and fail when the mean year returns decline.The developed method is applied to firm valuation to derive continuous-time equations for the firm present value and project NPV.
基金supported by the National Natural Science Foundation of China(11571262,11731012 and 11971361)。
文摘In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.
文摘A SEI model for hepatitis B is constructed where the susceptibility and other crucial transmission probabilities depend on the chronological age and the basic reproduction rate R0 is derived. Under suitable (biological and mathematical) assumptions in a closed population, results of Houpa D. D. E. et al. [1] are extended from constant case of p and q to age-dependent case: the disease-free equilibrium is globally asymptotically stable (GAS) if R0 . On the other hand, R0 > 1 induces that endemic equilibrium is GAS and the system is uniformly persistent.
文摘This paper outlines a two-stage assessment procedure for deriving probabilities of unique events.The calculations are illustrated using possible events pertaining to the Lehman failure in 2008.The procedures utilize pairwise comparisons associated with the Analytic Hierarchy Process.Typical betting odds are used to motivate an ordering of qualitative judgments that are then converted into quantitative assessments and finally a probability distribution.
文摘Decision-makers in unique or one-off situations may have difficulties in framing the probabilities of possible events that are required in modern decision-making. This paper illustrates a new approach to probability determination based on pairwise primary judgments on the relative likelihoods of the possible events. Related “news” on the situation can also be used to update these prior probabilities using Bayesian Revision. Illustrative calculations outline the entire process through to determination of posterior probabilities following a “news” event.
文摘Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.
文摘In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.
文摘Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relativistic effects are considered. The calculations are compared with other results in the literature. A good agreement is found. We also report on some unpublished energy values.
基金Federal Highway Administration at the University at Buffalo Under Contract Number DTFH61-08-C-00012
文摘The current AASHTO load and resistance factor design (LRFD) guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads (also referred to as multiple hazard or MH loads) can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions: (1) formulate the failure probabilities; (2) normalize various load distributions; and (3) establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.
基金Project supported by the National Natural Science Foundation of China (Grant No 40475007).
文摘Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the National Institute of Standards and Technology. The transition probability for a line of 424.18nm is reported for the first time. Meanwhile, a feasible method of calculating transition parameters related to special excited configurations or highly excited states is provided.
基金supported by the National Natural Science Foundation of China (10671149)the Ministry of Education of China, the Natural Science Foundation of Jiangxi(2008GQS0035)the Foundation of the Hubei Provincial Department of Education (B20091107)
文摘We consider a discrete time risk model in which the net payout (insurance risk) {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors (financial risk) {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278-1299).
基金supported by the Industrial Technology Development Program(B1120131046)。
文摘Configuration evaluation is a key technology to be considered in the design of multiple aircrafts formation(MAF)configurations with high dynamic properties in engineering applications.This paper deduces the relationship between relative velocity,dynamic safety distance and dynamic adjacent distance of formation members,then divides the formation states into collision-state and matching-state.Meanwhile,probability models are constructed based on the binary normal distribution of relative distance and relative velocity.Moreover,configuration evaluation strategies are studied by quantitatively analyzing the denseness and the basic capabilities according to the MAF collision-state probability and the MAF matching-state probability,respectively.The scale of MAF is grouped into 5 levels,and previous lattice-type structures are extended into four degrees by taking the relative velocities into account to instruct the configuration design under complex task conditions.Finally,hardware-in-loop(HIL)simulation and outfield flight test results are presented to verify the feasibility of these evaluation strategies.
基金supported by National NaturalScience Foundation of China(11971432)Natural Science Foundation of Zhejiang Province(LY21G010003)+1 种基金First Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics)the Natural Science Foundation of Chuzhou University(zrjz2019012)。
文摘Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.
文摘Factoring quadratics over Z is a staple of introductory algebra and textbooks tend to create the impression that doable factorizations are fairly common. To the contrary, if coefficients of a general quadratic are selected randomly without restriction, the probability that a factorization exists is zero. We achieve a specific quantification of the probability of factoring quadratics by taking a new approach that considers the absolute size of coefficients to be a parameter n. This restriction allows us to make relative likelihood estimates based on finite sample spaces. Our probability estimates are then conditioned on the size parameter n and the behavior of the conditional estimates may be studied as the parameter is varied. Specifically, we enumerate how many formal factored expressions could possibly correspond to a quadratic for a given size parameter. The conditional probability of factorization as a function of n is just the ratio of this enumeration to the total number of possible quadratics consistent with n. This approach is patterned after the well-known case where factorizations are carried out over a finite field. We review the finite field method as background for our method of dealing with Z [x]. The monic case is developed independently of the general case because it is simpler and the resulting probability estimating formula is more accurate. We conclude with a comparison of our theoretical probability estimates with exact data generated by a computer search for factorable quadratics corresponding to various parameter values.
文摘On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R,The theoretically predicted transition probabilities are in good agreement with the experimental ones.PACS numbers: 71.70.Ch, 78.20.Nv, 63.20.Mt, 63.20.