Particle method for the numerical simulation of the path-dependent McKean-Vlasov equation

TL;DR

This paper introduces a particle-based numerical method for simulating path-dependent McKean-Vlasov equations, providing explicit convergence rates and demonstrating its effectiveness through simulations of processes with memory.

Contribution

It develops a novel particle method for path-dependent McKean-Vlasov equations with proven convergence rates and practical demonstrations.

Findings

Explicit convergence rate established

Simulations of a memory-including Ornstein-Uhlenbeck process

Extension of neural mass model validated

Abstract

We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation, in which both the drift and the diffusion coefficients depend on the whole trajectory of the process up to the current time t, as well as on the corresponding marginal distributions. Our paper establishes an explicit convergence rate for this numerical approach. We illustrate our findings with numerical simulations of a modified Ornstein-Uhlenbeck process with memory, and of an extension of the Jansen-Rit mean-field model for neural mass.