Regular occupation measures of Volterra processes
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912981773713408 |
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| author | Friesen, Martin |
| author_facet | Friesen, Martin |
| contents | We introduce a local non-determinism condition for Volterra Itô processes that captures smoothing properties of possibly degenerate noise. By combining the stochastic sewing lemma with one-step Euler approximations, we first prove the joint space-time regularity for their occupation measure, self-intersection measure, and time marginals for such Volterra Itô processes. As an application, we obtain the space-time regularity of local times and self-intersection times for rough perturbations of Gaussian Volterra processes, and construct a class of non-Gaussian Volterra Iô processes that are $C^{\infty}$-regularising. Secondly, for the particular class of stochastic Volterra equations with Hölder continuous coefficients, using disintegration of measures for their Markovian lifts, we further establish the absolute continuity of finite-dimensional distributions. Finally, we prove the existence, uniqueness, and stability for self-interacting stochastic equations with distributional drifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular occupation measures of Volterra processes Friesen, Martin Probability We introduce a local non-determinism condition for Volterra Itô processes that captures smoothing properties of possibly degenerate noise. By combining the stochastic sewing lemma with one-step Euler approximations, we first prove the joint space-time regularity for their occupation measure, self-intersection measure, and time marginals for such Volterra Itô processes. As an application, we obtain the space-time regularity of local times and self-intersection times for rough perturbations of Gaussian Volterra processes, and construct a class of non-Gaussian Volterra Iô processes that are $C^{\infty}$-regularising. Secondly, for the particular class of stochastic Volterra equations with Hölder continuous coefficients, using disintegration of measures for their Markovian lifts, we further establish the absolute continuity of finite-dimensional distributions. Finally, we prove the existence, uniqueness, and stability for self-interacting stochastic equations with distributional drifts. |
| title | Regular occupation measures of Volterra processes |
| topic | Probability |
| url | https://arxiv.org/abs/2404.05381 |