# McKean-Vlasov limit for interacting systems with simultaneous jumps

## TL;DR

This paper establishes the McKean-Vlasov limit for systems of interacting diffusions with simultaneous jumps, providing a convergence rate for the empirical measures in mean-field models relevant to neuronal dynamics.

## Contribution

It introduces a coupling technique involving an intermediate process to prove propagation of chaos and quantify convergence rates in systems with jumps.

## Key findings

- Proves propagation of chaos for jump-diffusion systems.
- Provides explicit convergence rates in Wasserstein distance.
- Applicable to neuronal and other mean-field models.

## Abstract

Motivated by several applications, including neuronal models, we consider the McKean-Vlasov limit for mean-field systems of interacting diffusions with simultaneous jumps. We prove propagation of chaos via a coupling technique that involves an intermediate process and that gives a rate of convergence for the $W_1$ Wasserstein distance between the empirical measures of the two systems on the space of trajectories $\mathbf{D}([0,T],\mathbb{R}^d)$.