Propagation of Chaos for Weakly Interacting Mild Solutions to Stochastic Partial Differential Equations

TL;DR

This paper studies the propagation of chaos in weakly interacting solutions to semilinear SPDEs with non-Lipschitz coefficients, establishing conditions for existence, uniqueness, and continuity of solutions with distribution-dependent coefficients.

Contribution

It introduces new conditions for existence and uniqueness of McKean-Vlasov SPDEs and analyzes the propagation of chaos without requiring Lipschitz coefficients.

Findings

Established propagation of chaos under weaker conditions

Derived continuity and linear growth conditions for solutions

Extended analysis to distribution-dependent coefficients

Abstract

This article investigates the propagation of chaos property for weakly interacting mild solutions to semilinear stochastic partial differential equations whose coefficients might not satisfy Lipschitz conditions. Furthermore, we derive continuity and linear growth conditions for the existence and uniqueness of mild solutions to SPDEs with distribution dependent coefficients, so-called McKean-Vlasov SPDEs.