Articlegreen2021

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

39 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Stability and Control of Uncertain Systems Nonlinear Differential Equations Analysis

Abstract

In this paper we consider the stability for a type of stochastic McKean--Vlasov equation with non-Lipschitz coefficients. First, sufficient conditions are given for the exponential stability of second moments for their solutions in terms of a Lyapunov function. Then we weaken the conditions and furthermore obtain the 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.

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2024Stabilities of delay stochastic McKean-Vlasov equations in the G-framework 2025The Well-Posedness and Stabilities of Mean-Field Stochastic Differential Equations Driven by G-Brownian Motion 2022Stabilization of Stochastic McKean--Vlasov Equations with Feedback Control Based on Discrete-Time State Observation

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