Mean-field stochastic Volterra equations

TL;DR

This paper establishes well-posedness and propagation of chaos for multi-dimensional and one-dimensional mean-field stochastic Volterra equations under various regularity conditions, advancing the theoretical understanding of these complex stochastic systems.

Contribution

It provides new well-posedness results and quantitative propagation of chaos for mean-field stochastic Volterra equations with singular or regular kernels and coefficients.

Findings

Well-posedness established for multi-dimensional equations with Lipschitz coefficients.

Propagation of chaos results derived for systems with singular kernels.

Quantitative estimates provided for particle system convergence.

Abstract

The well-posedness is established for multi-dimensional mean-field stochastic Volterra equations with Lipschitz continuous coefficients and allowing for singular kernels as well as for one-dimensional mean-field stochastic Volterra equations with H\"older continuous diffusion coefficients and sufficiently regular kernels. In these different settings, quantitative, pointwise propagation of chaos results are derived for the associated Volterra type interacting particle systems.