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

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arxiv 2409.04377 v1 pith:2PHKMHOF submitted 2024-09-06 math.PR math.FAstat.ME

Olga Izyumtseva , Wasiur R. KhudaBukhsh This is my paper · ORCID
classification math.PRmath.FAstat.ME
keywords localprocessgaussiantimesvolterracontinuousexistencekernel
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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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