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arXiv · 1905.07883

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

Xiaojie Ding·Huijie Qiao
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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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BibTeXRIS

Xiaojie Ding, Huijie Qiao. 2019-05-20. Stability for Stochastic McKean-Vlasov Equations with Non-Lipschitz Coefficients. https://arxiv.org/abs/1905.07883

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