Stochastic Volterra equations with random functional coefficients in Banach spaces
Probability
2026-02-11 v1
Abstract
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.
Cite
@article{arxiv.2602.09922,
title = {Stochastic Volterra equations with random functional coefficients in Banach spaces},
author = {Alexander Kalinin},
journal= {arXiv preprint arXiv:2602.09922},
year = {2026}
}