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

Peng Xu () and Zhenlong Chen ()
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Peng Xu: Hangzhou City University
Zhenlong Chen: Zhejiang Gongshang University

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-26

Abstract: Abstract Let $$X=\{X(t),t\in \mathbb {R}^N\}$$ X = { X ( t ) , t ∈ 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.

Keywords: Anisotropic Gaussian field; Smoothness; Local time; Self-intersection local time; Sectorial local nondeterminism; 60G15; 60H05; 60H07 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01455-4

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