Local times of self-intersection and sample path properties of Volterra Gaussian processes
| Autor: | Izyumtseva, Olga, KhudaBukhsh, Wasiur R. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 25 pages, no figures |
| Databáze: | arXiv |
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