The existence and smoothness of self-intersection local time for a class of Gaussian processes

Lin Xie, Wenqing Ni, Shuicao Zheng and Guowei Lei

Statistics & Probability Letters, 2024, vol. 213, issue C

Abstract: In this paper sufficient conditions for the existence and smoothness of the self-intersection local time of a class of Gaussian processes are given in the sense of Meyer–Watanabe through L2 convergence and Wiener chaos expansion. Let X be a centered Gaussian process, whose canonical metric E[(X(t)−X(s)2)] is commensurate with σ2(|t−s|), where σ(⋅) is continuous, increasing and concave. If ∫0T1σ(γ)dγ<∞, then the self-intersection local time of the Gaussian process exists, and if ∫0T(σ(γ))−32dγ<∞, the self-intersection local time of the Gaussian process is smooth in the sense of Meyer–Watanabe.

Keywords: Self-intersection local time; Gaussian processes; Chaos expansion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110190

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