Euler scheme for density dependent stochastic differential equations

TL;DR

This paper establishes existence and uniqueness results for a class of density-dependent stochastic differential equations with bounded measurable drift, using Euler approximation and nonlinear Fokker-Planck equations, and applies these results to prove well-posedness.

Contribution

It introduces a novel approach combining Euler approximation and nonlinear Fokker-Planck equations to prove well-posedness of density-dependent SDEs with measurable drift.

Findings

Existence of solutions via Euler approximation.

Uniqueness established through nonlinear Fokker-Planck equation.

Well-posedness of the associated nonlinear Fokker-Planck equation.

Abstract

In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the associated nonlinear Fokker-Planck equation. As an application, we obtain the well-posedness of a nonlinear Fokker-Planck equation.