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Research on Statistic Characteristics of the Unbiased Estimation of hitting probability with Rectangle Objective Domain

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Research on Statistic Characteristics of the Unbiased Estima...

hitting Probabilities and Fractal Dimensions of Multiparameter Multifractional Brownian Motion

第25届中国控制与决策会议

作者： Wang Jun Li Yushan Guo Zhi School of Automation Nanjing University of Science and Technology China Baicheng Ordnance Test Center

ISBN: (纸本)9781467355339

With the assumption of shooting error distributed independently two-dimension normal, the traditional estimation of hitting probability with rectangle objective domain is biased. Based on an uniformly unbiased minimum variance method, in this paper the unbiased estimation of hitting probability with rectangle objective domain is compared with the traditional one, and the statistic characteristic of hitting probability is studied. Some examples are illustrated to prove that the unbiased estimation can reduce the amount of shells in test. The project of amount of shells are also provided for the test of first round hitting probability for tanks and armored vehicles.

关键词： unbiased estimation hitting probability rectangle objective domain Monte Carlo method

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Acta Mathematica Sinica,English Series 2013年第9期29卷 1723-1742页

作者： Zhen Long CHEN School of Statistics and Mathematics Zhejiang Gongshang University

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.

关键词： Multifractional Brownian motion hitting probability inverse image level set Hausdorff dimension packing dimension

hitting PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS

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Acta Mathematica Scientia 2022年第2期42卷 653-670页

作者： Jun WANG Zhenlong CHEN School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China School of Mathematics and Finance Chuzhou UniversityChuzhou 239000China

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 *** 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.

关键词： hitting probability multiple intersection anisotropic random field capacity Hausdorff dimension stochastic fractional heat equations

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

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Acta Mathematica Scientia 2011年第3期31卷 969-992页

作者：陈振龙 College of Statistics and Mathematics Zhejiang Gongshang University

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.

关键词： random string process hitting probability polar set Hausdorff dimension

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

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Acta Mathematica Scientia 2014年第1期34卷 141-161页

作者：陈振龙 College of Statistics and Mathematics Zhejiang Gongshang University

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.

关键词： intersection diffusion processes hitting probability polar set Hausdorffdimension

On intersections of independent anisotropic Gaussian random fields

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Science China Mathematics 2012年第11期55卷 2217-2232页

作者： CHEN ZhenLong XIAO YiMin School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Department of Statistics and probability Michigan State UniversityEast Lansing:MI 48824USA

Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.

关键词： intersection anisotropic Gaussian fields hitting probability Hausdorff dimension stochastic heatequation fractional Brownian sheet