Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs

Panpan Ren; Karl-Theodor Sturm; Feng-Yu Wang

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arXiv · 2110.06473

Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs

Panpan Ren·Karl-Theodor Sturm·Feng-Yu Wang

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Abstract

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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BibTeX RIS

Panpan Ren, Karl-Theodor Sturm, Feng-Yu Wang. 2021-10-13. Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs. https://arxiv.org/abs/2110.06473

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