Weak solutions to distribution-dependent stochastic Volterra equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908995368779776 |
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| author | Bergerhausen, Martin Prömel, David J. |
| author_facet | Bergerhausen, Martin Prömel, David J. |
| contents | We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels. To this end, we formulate an associated local martingale problem and establish its connection with weak solutions. Moreover, we derive continuity and integrability properties of the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak solutions to distribution-dependent stochastic Volterra equations Bergerhausen, Martin Prömel, David J. Probability We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels. To this end, we formulate an associated local martingale problem and establish its connection with weak solutions. Moreover, we derive continuity and integrability properties of the solutions. |
| title | Weak solutions to distribution-dependent stochastic Volterra equations |
| topic | Probability |
| url | https://arxiv.org/abs/2604.24390 |