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

2019/05/20 by Xiaojie Ding, Huijie Qiao, Ding, Xiaojie +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Stability and Controllability of Differential Equations #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1905.07883

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.

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• Well-posedness for path-dependent multivalued McKean-Vlasov stochastic differential equations

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