Local times of self-intersection and sample path properties of Volterra Gaussian processes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909307531952128 |
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| author | Izyumtseva, Olga KhudaBukhsh, Wasiur R. |
| author_facet | Izyumtseva, Olga KhudaBukhsh, Wasiur R. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_04377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local times of self-intersection and sample path properties of Volterra Gaussian processes Izyumtseva, Olga KhudaBukhsh, Wasiur R. Probability Functional Analysis Methodology 60J55, 60G15, 60G17, 60F17, 60F25 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. |
| title | Local times of self-intersection and sample path properties of Volterra Gaussian processes |
| topic | Probability Functional Analysis Methodology 60J55, 60G15, 60G17, 60F17, 60F25 |
| url | https://arxiv.org/abs/2409.04377 |