The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
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
The wind effects on steady-state scan characteristics and hit probability of terminal-sensitive projectile were discussed in this paper. Considering wind as the constitutions of the average wind and the impulsive wind...The wind effects on steady-state scan characteristics and hit probability of terminal-sensitive projectile were discussed in this paper. Considering wind as the constitutions of the average wind and the impulsive wind, a simplified wind field model was established for the ballistic calculation of the steady-state scan phase; under the windy condition, the effects of the range wind and the beam wind on the steady-state scan characteristics of the terminal-sensitive projectile were analyzed in detail and its hit probabilities for a certain armored target were calculated. The calculated results show that, when the wind speed exceeds a certain value, the hit probabilities of terminal-sensitive projectile drop rapidly; the wind effects must be considered in the application of the terminal-sensitive projectiles. This paper provides some theoretical references for the fire wind speed correction and the global structure optimization of the terminal-sensitive projectile.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
Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample pat...Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X (1) and X (2) are studied. More gener-ally, let E1, E2?(0,∞) and F ?Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1)∩X(2)(E2)∩F 6=?}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space (R+× R+× Rd,ρb), whereρb is an unsymmetric metric defined in R+× R+× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.展开更多
This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary condition...This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.展开更多
The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower...The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an (N, d)-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.展开更多
Let X = {X(t):t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measu...Let X = {X(t):t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.展开更多
基金the National Natural Science Foundation of China and the StateEducation of Commission Ph.D. Station Foundation
文摘The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.
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.
基金Sponsored by Doctoral Foundation of Ministry of Education of China (20093219120006)
文摘The wind effects on steady-state scan characteristics and hit probability of terminal-sensitive projectile were discussed in this paper. Considering wind as the constitutions of the average wind and the impulsive wind, a simplified wind field model was established for the ballistic calculation of the steady-state scan phase; under the windy condition, the effects of the range wind and the beam wind on the steady-state scan characteristics of the terminal-sensitive projectile were analyzed in detail and its hit probabilities for a certain armored target were calculated. The calculated results show that, when the wind speed exceeds a certain value, the hit probabilities of terminal-sensitive projectile drop rapidly; the wind effects must be considered in the application of the terminal-sensitive projectiles. This paper provides some theoretical references for the fire wind speed correction and the global structure optimization of the terminal-sensitive projectile.
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.
基金supported by National Natural Science Foundation of China(11371321)Zhejiang Provincial Natural Science Foundation of China(Y6100663)the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statis-tics of Zhejiang Gongshang University)
文摘Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X (1) and X (2) are studied. More gener-ally, let E1, E2?(0,∞) and F ?Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1)∩X(2)(E2)∩F 6=?}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space (R+× R+× Rd,ρb), whereρb is an unsymmetric metric defined in R+× R+× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.
基金supported by the Natural Science Foundation of Zhejiang Province(Y6100663)
文摘This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.
基金Supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y6100663)
文摘The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an (N, d)-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.
基金Supported by National Natural Science Foundation of China(Grant No.11371321)
文摘Let X = {X(t):t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.