Hitting Probabilities and the Hausdorff Dimension of the Inverse Images of a Class of Anisotropic Random Fields

作     者：Zhen Long CHEN Quan ZHOU 

作者机构：School of Statistics and MathematicsZhejiang Gongshang University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2015年第31卷第12期

页      面：1895-1922页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.11371321) 

主　　题：Anisotropic random field non-linear stochastic heat equations spatially homogeneous Gaussian noise hitting probabilities Hausdorff dimension inverse image 

摘      要：Let X = {X（t）：t ∈ R^N} be an anisotropic random field with values in R^*** 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 *** also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level *** 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.