The random step maneuver with uniformly distributed starting times has the disadvantage that it cannot focus the starting time on the more efficiency time. It decreases the penetration probability. To resolve this pro...The random step maneuver with uniformly distributed starting times has the disadvantage that it cannot focus the starting time on the more efficiency time. It decreases the penetration probability. To resolve this problem, a random step penetration algorithm with normal distribution starting time is proposed. Using the shaping filters and adjoint system method, the miss distance with different starting times can be acquired. According to the penetration standard, the time window ensuring successful penetration can be calculated and it is used as the 3σ bound of the normally distributed random maneuver. Simulation results indicate that the normally distributed random maneuver has higher penetration probability than the uniformly distributed random maneuver.展开更多
The reasons of the static strength dispersion and the fatigue life dispersion of composite laminates are analyzed in this article. It is concluded that the inner original defects, which derived from the manufacturing ...The reasons of the static strength dispersion and the fatigue life dispersion of composite laminates are analyzed in this article. It is concluded that the inner original defects, which derived from the manufacturing process of composite laminates, are the common and major reason of causing the random distributions of the static strength and the fatigue life. And there is a correlative relation between the two distributions. With the study of statistical relationship between the fatigue loading and the fatigue life in the uniform confidence level and the same survival rate S-N curves of material, the relationship between the static strength distribution and the fatigue life distribution through a material S-N curve model has been obtained. And then the model which is used to describe the distributions of fatigue life of composites, based on their distributions of static strength, is set up. This model reasonably reflects the effects of the inner original defects on the static strength dispersion and on the fatigue life dispersion of composite laminates. The experimental data of three kinds of composite laminates are employed to verify this model, and the results show that this model can predict the random distributions of fatigue life for composites under any fatigue loads fairly well.展开更多
Simultaneous bandwidth(BW) enhancement and time-delay signature(TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers(MCSLs) with random optical injection are prop...Simultaneous bandwidth(BW) enhancement and time-delay signature(TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers(MCSLs) with random optical injection are proposed and numerically investigated. The influences of system parameters on TDS suppression(characterized by autocorrelation function(ACF) and permutation entropy(PE) around characteristic time) and chaos BW are investigated. The results show that, with the increasing bias current, the ranges of parameters(detuning and injection strength) for the larger BW(> 20 GHz) are broadened considerably, while the parameter range for optimized TDS(< 0.1) is not shrunk obviously.Under optimized parameters, the system can simultaneously achieve two chaos outputs with enhanced BW(> 20 GHz)and perfect TDS suppression. In addition, the system can generate two-channel high-speed truly physical random number sequences at 200 Gbits/s for each channel.展开更多
The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random t...The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.展开更多
In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),...In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions.展开更多
Wireless Sensor Networks (WSN) have recently become one of the major research areas in the wireless communication field and are implemented in a variety of applications. One of these applications that will be tackled ...Wireless Sensor Networks (WSN) have recently become one of the major research areas in the wireless communication field and are implemented in a variety of applications. One of these applications that will be tackled in this paper is monitoring electromagnetic (EM) pollution that is mostly caused by a variety of wireless devices that we use in our daily life. This paper presents a generic algorithm that uses a WSN to monitor EM hazardous emissions and reports variation caused by four violators. Additionally it calculates the network’s lifetime and simultaneously studies the effect of random parameters and their distributions on the network. Finally the different combinations of the random parameters and the altered distributions are compared together to achieve the combination that can prolong the network’s lifetime.展开更多
An all-fiberized random distributed feedback Raman fiber laser(RRFL)with LP_(11) mode output at 1134 nm has been demonstrated experimentally,where an intracavity acoustically induced fiber grating is employed for moda...An all-fiberized random distributed feedback Raman fiber laser(RRFL)with LP_(11) mode output at 1134 nm has been demonstrated experimentally,where an intracavity acoustically induced fiber grating is employed for modal switching.The maximum output power of LP_(11) mode is 93.8 W with the modal purity of 82%,calculated by numerical mode decomposition technology based on stochastic parallel-gradient descent algorithm.To our best knowledge,this is the highest output power with high purity of LP_(11) mode generated from the RRFL.This work may pave a path towards advanced fiber lasers with special temporal and spatial characteristics for applications.展开更多
Behavior affects an individual's life in all aspects,e.g.,enhancing fitness,leveraging predation risk,and reducing competition with conspecifics.However,the sequential distribution of behaviors received less atten...Behavior affects an individual's life in all aspects,e.g.,enhancing fitness,leveraging predation risk,and reducing competition with conspecifics.However,the sequential distribution of behaviors received less attention and is unclear what the function of displacement behavior is.Displacement activities can be found in vertebrate species but there is no formal method to determine whether a behavior is expressed as a displaced or normal activity.Analyzing the sequential distributions of behaviors in a natural setting may allow researchers to identify unexpected distributions as a possible signature of displacement activities.In this study,we used a behavior random permutation model to detect the presence of a displacement activity in the Tibetan antelope Pantholops hodgsonii and the Tibetan gazelle Procapra picticaudata.The results showed that grooming in both ungulates tended to be accompanied with vigilance,and the frequency of grooming after vigilance was significantly higher than before vigilance.A significant positive correlation between the scan rate and grooming rate in the 2 ungulates was obtained.We suggest that grooming could sometimes be expressed as a displacement activity in ungulates.In addition to providing a general method for further research on displacement activities in a variety of animal species,this study sheds light on the importance of a spectral analysis of sequential distribution of animal behaviors.Behavior random permutation models can be used to explore the relevance between any 2 behaviors in a specific sequence,especially to identify a myriad of unexpected behaviors relative to their normal context of occurrence.展开更多
Cuckoo search (CS), inspired by the obligate brood parasitic behavior of some cuckoo species, iteratively uses L6vy flights random walk (LFRW) and biased/selective random walk (BSRW) to search for new solutions....Cuckoo search (CS), inspired by the obligate brood parasitic behavior of some cuckoo species, iteratively uses L6vy flights random walk (LFRW) and biased/selective random walk (BSRW) to search for new solutions. In this study, we seek a simple strategy to set the scaling factor in LFRW, which can vary the scaling factor to achieve better performance. However, choosing the best scaling factor for each problem is intractable. Thus, we propose a varied scal- ing factor (VSF) strategy that samples a value from the range [0,1] uniformly at random for each iteration. In addition, we integrate the VSF strategy into several advanced CS vari- ants. Extensive experiments are conducted on three groups of benchmark functions including 18 common test functions, 25 functions proposed in CEC 2005, and 28 functions intro- duced in CEC 2013. Experimental results demonstrate the ef- fectiveness of the VSF strategy.展开更多
For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergenc...For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE(max1≤k≤n|Sk|^1/q-∈bn^1/qp)^+〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 (log n) ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.展开更多
Based on the concept of ubiquitiform,a ubiquitiformal crack extension model is developed for quasi-brittle materials.Numerical simulations are carried out using the ABAQUS software with the XFEM-based cohesive segment...Based on the concept of ubiquitiform,a ubiquitiformal crack extension model is developed for quasi-brittle materials.Numerical simulations are carried out using the ABAQUS software with the XFEM-based cohesive segments method to determine the ubiquitiformal crack extension path or fracture surface profile of the material under quasi-static loading.Such a ubiquitiformal crack model removes the singularity of a fractal crack;for the latter,the boundary value problem cannot be uniquely defined.In the simulation,the material properties,e.g.,the tensile strength,are assumed to obey the Weibull distribution.The meso-element equivalent method is used to determine the correlation between the Weibull distribution parameters and the aggregate gradation of concrete materials.The numerical results show that the complexities of the ubiquitiformal crack configurations are in good agreement with the previous experimental data.Through the numerical simulation,it is further demonstrated that the complexity of a ubiquitiformal crack is insensitive to the random spatial distribution of the aggregates,but more dependent on the Weibull distribution parameters which reflect the heterogeneity of the concrete.展开更多
The distribution law of the random code structure of randomly constructed irregular low-density parity-check (LDPC) codes is studied, Based on the Progressive Edge-Growth (PEG) algorithm, a new algorithm which can...The distribution law of the random code structure of randomly constructed irregular low-density parity-check (LDPC) codes is studied, Based on the Progressive Edge-Growth (PEG) algorithm, a new algorithm which can both ellminate short cycles and keep the distribution of the random code structure is presented, The experimentsl results show that the performance of the irregular LDPC codes constructed by the new algorithm is superior to that of the PEG algorithm,展开更多
In this paper,an exponential inequality for weighted sums of identically distributed NOD (negatively orthant dependent) random variables is established,by which we obtain the almost sure convergence rate of which re...In this paper,an exponential inequality for weighted sums of identically distributed NOD (negatively orthant dependent) random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.展开更多
A batch Markov arrival process(BMAP) X^*=(N, J) is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process i...A batch Markov arrival process(BMAP) X^*=(N, J) is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper,a new and inverse problem is proposed firstly: given a Markov chain J, can we deploy a process N such that the 2-dimensional process X^*=(N, J) is a BMAP? The process X^*=(N, J) is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed(i.i.d) random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic(D_k, k = 0, 1, 2· · ·)and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.展开更多
文摘The random step maneuver with uniformly distributed starting times has the disadvantage that it cannot focus the starting time on the more efficiency time. It decreases the penetration probability. To resolve this problem, a random step penetration algorithm with normal distribution starting time is proposed. Using the shaping filters and adjoint system method, the miss distance with different starting times can be acquired. According to the penetration standard, the time window ensuring successful penetration can be calculated and it is used as the 3σ bound of the normally distributed random maneuver. Simulation results indicate that the normally distributed random maneuver has higher penetration probability than the uniformly distributed random maneuver.
文摘The reasons of the static strength dispersion and the fatigue life dispersion of composite laminates are analyzed in this article. It is concluded that the inner original defects, which derived from the manufacturing process of composite laminates, are the common and major reason of causing the random distributions of the static strength and the fatigue life. And there is a correlative relation between the two distributions. With the study of statistical relationship between the fatigue loading and the fatigue life in the uniform confidence level and the same survival rate S-N curves of material, the relationship between the static strength distribution and the fatigue life distribution through a material S-N curve model has been obtained. And then the model which is used to describe the distributions of fatigue life of composites, based on their distributions of static strength, is set up. This model reasonably reflects the effects of the inner original defects on the static strength dispersion and on the fatigue life dispersion of composite laminates. The experimental data of three kinds of composite laminates are employed to verify this model, and the results show that this model can predict the random distributions of fatigue life for composites under any fatigue loads fairly well.
基金Project supported by the Sichuan Science and Technology Program,China(Grant No.2019YJ0530)the Scientific Research Fund of Sichuan Provincial Education Department,China(Grant No.18ZA0401)+1 种基金the Innovative Training Program for College Student of Sichuan Normal University,China(Grant No.S20191063609)the National Natural Science Foundation of China(Grant No.61205079)。
文摘Simultaneous bandwidth(BW) enhancement and time-delay signature(TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers(MCSLs) with random optical injection are proposed and numerically investigated. The influences of system parameters on TDS suppression(characterized by autocorrelation function(ACF) and permutation entropy(PE) around characteristic time) and chaos BW are investigated. The results show that, with the increasing bias current, the ranges of parameters(detuning and injection strength) for the larger BW(> 20 GHz) are broadened considerably, while the parameter range for optimized TDS(< 0.1) is not shrunk obviously.Under optimized parameters, the system can simultaneously achieve two chaos outputs with enhanced BW(> 20 GHz)and perfect TDS suppression. In addition, the system can generate two-channel high-speed truly physical random number sequences at 200 Gbits/s for each channel.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372156 and 61405053)the Natural Science Foundation of Zhejiang Province of China(Grant No.LZ13F04001)
文摘The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.
文摘In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions.
文摘Wireless Sensor Networks (WSN) have recently become one of the major research areas in the wireless communication field and are implemented in a variety of applications. One of these applications that will be tackled in this paper is monitoring electromagnetic (EM) pollution that is mostly caused by a variety of wireless devices that we use in our daily life. This paper presents a generic algorithm that uses a WSN to monitor EM hazardous emissions and reports variation caused by four violators. Additionally it calculates the network’s lifetime and simultaneously studies the effect of random parameters and their distributions on the network. Finally the different combinations of the random parameters and the altered distributions are compared together to achieve the combination that can prolong the network’s lifetime.
基金supported by the National Natural Science Foundation of China(Nos.11704409,62061136013,and 12174445)the Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology(No.SKL2020KF03)the Special Fund for Hunan Provincial Innovative Province Building(No.2019RS3017)。
文摘An all-fiberized random distributed feedback Raman fiber laser(RRFL)with LP_(11) mode output at 1134 nm has been demonstrated experimentally,where an intracavity acoustically induced fiber grating is employed for modal switching.The maximum output power of LP_(11) mode is 93.8 W with the modal purity of 82%,calculated by numerical mode decomposition technology based on stochastic parallel-gradient descent algorithm.To our best knowledge,this is the highest output power with high purity of LP_(11) mode generated from the RRFL.This work may pave a path towards advanced fiber lasers with special temporal and spatial characteristics for applications.
基金Authors thank the Tibet Major Science and Technology Project(XZ201901-GA-06)National Natural Science Foundation of China(grant nos.31360141 and 31772470)West Light Foundation of Chinese Academy of Sciences(2015)in supporting the study financially.
文摘Behavior affects an individual's life in all aspects,e.g.,enhancing fitness,leveraging predation risk,and reducing competition with conspecifics.However,the sequential distribution of behaviors received less attention and is unclear what the function of displacement behavior is.Displacement activities can be found in vertebrate species but there is no formal method to determine whether a behavior is expressed as a displaced or normal activity.Analyzing the sequential distributions of behaviors in a natural setting may allow researchers to identify unexpected distributions as a possible signature of displacement activities.In this study,we used a behavior random permutation model to detect the presence of a displacement activity in the Tibetan antelope Pantholops hodgsonii and the Tibetan gazelle Procapra picticaudata.The results showed that grooming in both ungulates tended to be accompanied with vigilance,and the frequency of grooming after vigilance was significantly higher than before vigilance.A significant positive correlation between the scan rate and grooming rate in the 2 ungulates was obtained.We suggest that grooming could sometimes be expressed as a displacement activity in ungulates.In addition to providing a general method for further research on displacement activities in a variety of animal species,this study sheds light on the importance of a spectral analysis of sequential distribution of animal behaviors.Behavior random permutation models can be used to explore the relevance between any 2 behaviors in a specific sequence,especially to identify a myriad of unexpected behaviors relative to their normal context of occurrence.
文摘Cuckoo search (CS), inspired by the obligate brood parasitic behavior of some cuckoo species, iteratively uses L6vy flights random walk (LFRW) and biased/selective random walk (BSRW) to search for new solutions. In this study, we seek a simple strategy to set the scaling factor in LFRW, which can vary the scaling factor to achieve better performance. However, choosing the best scaling factor for each problem is intractable. Thus, we propose a varied scal- ing factor (VSF) strategy that samples a value from the range [0,1] uniformly at random for each iteration. In addition, we integrate the VSF strategy into several advanced CS vari- ants. Extensive experiments are conducted on three groups of benchmark functions including 18 common test functions, 25 functions proposed in CEC 2005, and 28 functions intro- duced in CEC 2013. Experimental results demonstrate the ef- fectiveness of the VSF strategy.
基金supported by National Natural Science Foundation of China (Grant No. 10871146)supported by Natural Sciences and Engineering Research Council of Canada
文摘For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE(max1≤k≤n|Sk|^1/q-∈bn^1/qp)^+〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 (log n) ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.
基金This work was supported by the National Natural Science Foundation of China(11772056)。
文摘Based on the concept of ubiquitiform,a ubiquitiformal crack extension model is developed for quasi-brittle materials.Numerical simulations are carried out using the ABAQUS software with the XFEM-based cohesive segments method to determine the ubiquitiformal crack extension path or fracture surface profile of the material under quasi-static loading.Such a ubiquitiformal crack model removes the singularity of a fractal crack;for the latter,the boundary value problem cannot be uniquely defined.In the simulation,the material properties,e.g.,the tensile strength,are assumed to obey the Weibull distribution.The meso-element equivalent method is used to determine the correlation between the Weibull distribution parameters and the aggregate gradation of concrete materials.The numerical results show that the complexities of the ubiquitiformal crack configurations are in good agreement with the previous experimental data.Through the numerical simulation,it is further demonstrated that the complexity of a ubiquitiformal crack is insensitive to the random spatial distribution of the aggregates,but more dependent on the Weibull distribution parameters which reflect the heterogeneity of the concrete.
基金Supported by the National Natural Science Foundation of China (Grant No. 60172030)Huawei Science FoundationXidian ISN National Key Laboratory
文摘The distribution law of the random code structure of randomly constructed irregular low-density parity-check (LDPC) codes is studied, Based on the Progressive Edge-Growth (PEG) algorithm, a new algorithm which can both ellminate short cycles and keep the distribution of the random code structure is presented, The experimentsl results show that the performance of the irregular LDPC codes constructed by the new algorithm is superior to that of the PEG algorithm,
基金Supported by the National Natural Science Foundation of China ( 11061007)
文摘In this paper,an exponential inequality for weighted sums of identically distributed NOD (negatively orthant dependent) random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.
基金Supported by the National Natural Science Foundation of China(No.11671132,11601147)Hunan Provincial Natural Science Foundation of China(No.16J3010)+1 种基金Philosophy and Social Science Foundation of Hunan Province(No.16YBA053)Key Scientific Research Project of Hunan Provincial Education Department(No.15A032)
文摘A batch Markov arrival process(BMAP) X^*=(N, J) is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper,a new and inverse problem is proposed firstly: given a Markov chain J, can we deploy a process N such that the 2-dimensional process X^*=(N, J) is a BMAP? The process X^*=(N, J) is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed(i.i.d) random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic(D_k, k = 0, 1, 2· · ·)and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.