Density Dependent Singular Stochastic Differential Equations

TL;DR

This paper establishes well-posedness results for a class of singular density-dependent stochastic differential equations, including reflecting variants, under local integrability and Lipschitz conditions.

Contribution

It proves strong and weak well-posedness for singular SDEs depending on distribution densities, extending the theory to density-dependent reflecting SDEs.

Findings

Well-posedness of singular density-dependent SDEs established

Results include both strong and weak solutions

Includes analysis of density-dependent reflecting SDEs

Abstract

The (strong and weak) well-posedness is proved for singular SDEs depending on the distribution density point-wisely and globally, where the drift satisfies a local integrability condition in time-spatial variables, and is Lipschitz continuous in the distribution density with respect to a local $L^k$-norm. Density dependent reflecting SDEs are also studied.