Simulation of particle systems interacting through hitting times
classification
🧮 math.NA
math.PR
keywords
hittingorderparticlesimulationarisingassumptionsblow-upboundary
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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.
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