Existence and smoothness of density function of solution to Mckean--Vlasov Equation with general coefficients
Analysis of PDEs
2025-04-11 v1
Abstract
In this paper, we study the existence and smoothness of a density function to the solution of a Mckean-Vlasov equation with the aid of Malliavin calculus. We first show the existence of the density function under assumptions that the coefficients of equation are only Lipschitz continuity and satisfy a uniform elliptic condition. Furthermore, we derive a precise regularity order and bounded a priori estimate for the density function under optimal smoothness assumptions for the coefficients. Finally, we present several numerical experiments to illustrate the approximation of the density function independently determined by solving a Fokker-Planck equation.
Keywords
Cite
@article{arxiv.2504.07368,
title = {Existence and smoothness of density function of solution to Mckean--Vlasov Equation with general coefficients},
author = {Boyu Wang and Yongkui Zou and Jinhui Zhou},
journal= {arXiv preprint arXiv:2504.07368},
year = {2025}
}