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arXiv · 2409.04377

Local times of self-intersection and sample path properties of Volterra Gaussian processes

Olga Izyumtseva·Wasiur R. KhudaBukhsh
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Abstract

We study a Volterra Gaussian process of the form $X(t)=\int^t_0K(t,s)d{W(s)},$ where $W$ is a Wiener process and $K$ is a continuous kernel. In dimension one, we prove a law of the iterated logarithm, discuss the existence of local times and verify a continuous dependence between the local time and the kernel that generates the process. Furthermore, we prove the existence of the Rosen renormalized self-intersection local times for a planar Gaussian Volterra process.

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Olga Izyumtseva, Wasiur R. KhudaBukhsh. 2024-09-06. Local times of self-intersection and sample path properties of Volterra Gaussian processes. https://arxiv.org/abs/2409.04377

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