Long time behavior of stochastic Mckean-Vlasov equations

Article Mathematics, Applied

Exponential convergence in entropy and Wasserstein for McKean-Vlasov SDEs

Panpan Ren et al.

Summary: The study demonstrates exponential convergence in certain granular media type equations for McKean-Vlasov SDEs, involving relative entropy and Wasserstein distance.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2021)

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Article Mathematics, Applied

Polynomial stability of highly non-linear time-changed stochastic differential equations

Wei Liu

Summary: This study investigates the moment stability of a class of time-changed stochastic differential equations with coefficients allowed to grow super-linearly. It is shown that the decay rate is polynomial for certain types of subordinators, which differs significantly from classical SDEs driven by Brownian motion.

APPLIED MATHEMATICS LETTERS (2021)

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Article Statistics & Probability

Path-distribution dependent SDEs with singular coefficients

Xing Huang

Summary: This paper establishes the existence and uniqueness for path-dependent McKean-Vlasov type SDEs with integrability conditions, and derives gradient estimates and Harnack type inequalities under the assumption that the drifts are Dini continuous in the space variable. These results generalize those obtained for classical functional SDEs with singular coefficients.

ELECTRONIC JOURNAL OF PROBABILITY (2021)

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Article Automation & Control Systems

STABILITY FOR STOCHASTIC MCKEAN-VLASOV EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS

Xiaojie Ding et al.

Summary: This paper examines the stability of a type of stochastic McKean-Vlasov equation with non-Lipschitz coefficients. It provides conditions for the exponential stability of second moments for their solutions and proves the almost surely asymptotic stability of their solutions. The choice of Lyapunov functions is motivated by an example given in the paper.

SIAM JOURNAL ON CONTROL AND OPTIMIZATION (2021)

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Article Statistics & Probability