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Hitting Probabilities and the Hausdorff Dimension of the Inverse Images of a Class of Anisotropic Random Fields 被引量:1

Hitting Probabilities and the Hausdorff Dimension of the Inverse Images of a Class of Anisotropic Random Fields
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摘要 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. 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.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第12期1895-1922,共28页 数学学报(英文版)
基金 Supported by National Natural Science Foundation of China(Grant No.11371321)
关键词 Anisotropic random field non-linear stochastic heat equations spatially homogeneous Gaussian noise hitting probabilities Hausdorff dimension inverse image Anisotropic random field non-linear stochastic heat equations spatially homogeneous Gaussian noise hitting probabilities Hausdorff dimension inverse image
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