Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations

TL;DR

This paper introduces a novel particle system algorithm for non-conservative McKean-type stochastic differential equations, analyzing chaos propagation and convergence to regularized nonlinear PDE solutions.

Contribution

It presents an original interacting particle system and demonstrates its propagation of chaos and convergence properties for non-conservative McKean SDEs.

Findings

Particle system effectively models non-conservative McKean SDEs

Time-discretized approximation converges to PDE solutions

Propagation of chaos is established for the proposed system

Abstract

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE.