Simulation of particle systems interacting through hitting times
Provides a numerical method for mean-field models with hitting-time feedback, relevant for applications in finance or biology.
Developed an Euler-type particle method for simulating a McKean-Vlasov equation with positive feedback from hitting a boundary, achieving convergence order 1/2 in time step, improved to order 1 with Brownian bridges and local mesh refinement.
We develop an Euler-type particle method for the simulation of a McKean--Vlasov equation arising from a mean-field model with positive feedback from hitting a boundary. Under assumptions on the parameters which ensure differentiable solutions, we establish convergence of order $1/2$ in the time step. Moreover, we give a modification of the scheme using Brownian bridges and local mesh refinement, which improves the order to $1$. We confirm our theoretical results with numerical tests and empirically investigate cases with blow-up.