Smoothness of Local times and Self-Intersection Local Times of Space-Time Anisotropic Gaussian Random Fields

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发表日期：

2025年10月10日

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Peng Xu,
Zhenlong Chen

摘要

Let $X=\{X(t),t\in \mathbb {R}^N\}$ $X = {X (t), t \in R^{N}}$ be a centered space-time anisotropic Gaussian random field with values in $\mathbb {R}^d$ $R^{d}$ . Under some general conditions, sufficient and necessary conditions for the existence and sufficient conditions for the smoothness (in the sense of Meyer–Watanabe) of the local times, collision local times, intersection local times, and self-intersection local times are established for X. The existing results of fractional Brownian sheets and other Gaussian random fields are extended to space-time anisotropic Gaussian random fields under sectorial local nondeterminism.