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Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs

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arxiv 2110.06473 v2 pith:PZRQIJWU submitted 2021-10-13 math.PR

Panpan Ren , Karl-Theodor Sturm , Feng-Yu Wang This is my paper · ORCID
classification math.PR
keywords sdescasedistancefunctionwassersteincostdissipativeergodicity
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As extensions to the corresponding results derived for time homogeneous McKean- Vlasov SDEs, the exponential ergodicity is proved for time-periodic distribution dependent SDEs in three different situations: 1) in the quadratic Wasserstein distance and relative entropy for the dissipative case; 2) in the Wasserstein distance induced by a cost function for the partially dissipative case; and 3) in the weighted Wasserstein distance induced by a cost function and a Lyapunov function for the fully non-dissipative case. The main results are illustrated by time inhomogeneous granular media equations, and are extended to reflecting McKean-Vlasov SDEs in a convex domain.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions

    math.DS 2025-01 reject novelty 5.0 of 10

    Under periodic distribution-dependent Lyapunov conditions, the paper constructs T-periodic solutions for McKean-Vlasov SDEs by lifting the dynamics to the product space R^d times P(R^d).

  2. Pullback measure attractors and limiting behaviors of McKean-Vlasov stochastic delay lattice systems

    math.DS 2024-12 conditional novelty 5.0 of 10

    Pullback measure attractors exist uniquely for non-autonomous McKean-Vlasov stochastic delay lattice systems, are singleton and exponentially mixing under stronger damping, and are upper semicontinuous as distribution...

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