On McKean-Vlasov Branching Diffusion Processes

TL;DR

This paper investigates McKean-Vlasov branching diffusion processes, establishing existence, uniqueness, and propagation of chaos, and connecting the mean-field limit with large population models.

Contribution

It provides the first comprehensive analysis of McKean-Vlasov branching diffusions, including strong and weak formulations, existence, uniqueness, and propagation of chaos results.

Findings

Existence and uniqueness of solutions established

Weak solution and martingale problem formulated

Propagation of chaos demonstrated for large populations

Abstract

We study a nonlinear branching diffusion process in the sense of McKean, i.e., where particles are subjected to a mean-field interaction. We consider first a strong formulation of the problem and we provide an existence and uniqueness result by using contraction arguments. Then we consider the notion of weak solution and its equivalent martingale problem formulation. In this setting, we provide a general weak existence result, as well as a propagation of chaos property, i.e., the McKean-Vlasov branching diffusion is the limit of a large population branching diffusion process with mean-field interaction.