Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet
Probability
2024-05-01 v1
Abstract
In this paper, we consider a McKean-Vlasov (mean-field) stochastic partial differential equations (SPDEs) driven by a Brownian sheet. We study the propagation of chaos for a space-time Ornstein-Uhlenbeck SPDE type. Subsequently, we prove the existence and uniqueness of a nonlinear McKean-Vlasov SPDE. Finally, we establish a Fokker-Planck equation for the law of the solution of the McKean-Vlasov type SPDE driven by a time-space Brownian sheet, and we provide some examples to illustrate the results obtained.
Cite
@article{arxiv.2404.19490,
title = {Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet},
author = {Nacira Agram and Bernt Oksendal and Frank Proske and Olena Tymoshenko},
journal= {arXiv preprint arXiv:2404.19490},
year = {2024}
}