Sample Path Properties of Anisotropic Gaussian Random Fields
Sample Path Properties of Anisotropic Gaussian Random Fields
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DOI：
10.1007/978-3-540-85994-9_5
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Yimin Xiao
中科院分区：
文献类型：
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作者：
Yimin Xiao
各向异性高斯随机场出现在概率论和各种应用中。典型的例子是分数布朗片、具有平稳增量的算子缩放高斯场以及随机热方程的解。本文主要关注各向异性高斯随机场的样本路径属性。假设是一个高斯随机场，其值为 Rd 和参数 H1,…,HN。我们的目标是明确地表征X的参数的各向异性性质。在一些一般条件下，我们建立了各向异性高斯随机场的连续模、小球概率、分形维数、命中概率和局部时间的结果。我们研究的一个重要工具是各种形式的强局部非决定论。
Anisotropic Gaussian random fields arise in probability theory and in various applications. Typical examples are fractional Brownian sheets, operator-scaling Gaussian fields with stationary increments, and the solution to the stochastic heat equation.This paper is concerned with sample path properties of anisotropic Gaussian random fields in general. Letbe a Gaussian random field with values in Rdand with parameters H1,…,HN. Our goal is to characterize the anisotropic nature ofXin terms of its parameters explicitly.Under some general conditions, we establish results on the modulus of continuity, small ball probabilities, fractal dimensions, hitting probabilities and local times of anisotropic Gaussian random fields. An important tool for our study is the various forms of strong local nondeterminism.