Rate of homogenization for fully-coupled McKean-Vlasov SDEs
Probability
2022-08-24 v3
Abstract
We consider a fully-coupled slow-fast system of McKean-Vlasov SDEs with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy-Problem on the Wasserstein space that are of independent interest.
Keywords
Cite
@article{arxiv.2202.07753,
title = {Rate of homogenization for fully-coupled McKean-Vlasov SDEs},
author = {Zachary Bezemek and Konstantinos Spiliopoulos},
journal= {arXiv preprint arXiv:2202.07753},
year = {2022}
}
Comments
42 pages, 1 figure. To appear in Stochastics and Dynamics