# Stability for Stochastic McKean-Vlasov Equations with Non-Lipschitz Coefficients

## TL;DR

This paper investigates the stability properties of stochastic McKean-Vlasov equations with non-Lipschitz coefficients, providing conditions for exponential stability, boundedness, and almost sure asymptotic stability of solutions.

## Contribution

It introduces new stability criteria for stochastic McKean-Vlasov equations with non-Lipschitz coefficients, including Lyapunov-based conditions and weakened assumptions.

## Key findings

- Exponential stability of second moments established.
- Solutions are shown to be exponentially 2-ultimately bounded.
- Almost surely asymptotic stability proved.

## Abstract

In this paper we consider the stability for a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. First, sufficient conditions are given for the exponential stability of the second moments for their solutions in terms of a Lyapunov function. Then we weaken the conditions and furthermore obtain exponentially 2-ultimate boundedness of their solutions. After this, the almost surely asymptotic stability of their solutions is proved. Finally we give an example to motivate the choice of Lyapunov functions.