Stochastic Volterra equations with random functional coefficients in Banach spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914319532294144 |
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| author | Kalinin, Alexander |
| author_facet | Kalinin, Alexander |
| contents | We derive unique Banach-valued solutions to stochastic Volterra equations with random coefficients that may depend on pure chance and involve singular kernels. In particular, for controlled and distribution-dependent coefficients these solutions become strong, as a measurability analysis of the Wasserstein metric confirms. The presented novel approach is based on the proof that a stochastic Volterra integral admits a progressively measurable modification in a weak sense and on sharp moment estimates for non-negative product measurable processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09922 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Volterra equations with random functional coefficients in Banach spaces Kalinin, Alexander Probability 60H20, 60H30, 60G17, 45D05 We derive unique Banach-valued solutions to stochastic Volterra equations with random coefficients that may depend on pure chance and involve singular kernels. In particular, for controlled and distribution-dependent coefficients these solutions become strong, as a measurability analysis of the Wasserstein metric confirms. The presented novel approach is based on the proof that a stochastic Volterra integral admits a progressively measurable modification in a weak sense and on sharp moment estimates for non-negative product measurable processes. |
| title | Stochastic Volterra equations with random functional coefficients in Banach spaces |
| topic | Probability 60H20, 60H30, 60G17, 45D05 |
| url | https://arxiv.org/abs/2602.09922 |