On Lyapunov Conditions for the Well-Posedness of McKean-Vlasov Stochastic Differential Delay Equations

TL;DR

This paper establishes conditions under which McKean-Vlasov stochastic differential delay equations have unique solutions, extending the understanding of their well-posedness through Lyapunov methods and Lipschitz conditions.

Contribution

It introduces a Lyapunov-based approach combined with Lipschitz conditions to prove the existence and uniqueness of solutions for these delay equations.

Findings

Existence of unique solutions under specified conditions

Lyapunov conditions ensure well-posedness

Extension of classical results to delay equations

Abstract

This work focuses on the well-posedness of McKean-Vlasov stochastic differential delay equations. Under suitable lipschitz conditions on the drift and diffusion terms, along with a distribution dependent Lyapunov condition, this paper shows the existence of a unique solution to the distribution dependent stochastic differential delay equation.