English

Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs

Probability 2023-10-03 v2

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.

Keywords

Cite

@article{arxiv.2110.06473,
  title  = {Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs},
  author = {Panpan Ren and Karl-Theodor Sturm and Feng-Yu Wang},
  journal= {arXiv preprint arXiv:2110.06473},
  year   = {2023}
}

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21pages