Weak solutions to distribution-dependent stochastic Volterra equations

Martin Bergerhausen; David J. Prömel

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arXiv · 2604.24390

Weak solutions to distribution-dependent stochastic Volterra equations

Martin Bergerhausen·David J. Prömel

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Abstract

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.

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Martin Bergerhausen, David J. Prömel. 2026-04-27. Weak solutions to distribution-dependent stochastic Volterra equations. https://arxiv.org/abs/2604.24390

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