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

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.