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arXiv · 2404.19490

Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet

Nacira Agram·Bernt Oksendal·Frank Proske·Olena Tymoshenko
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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.

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Nacira Agram, Bernt Oksendal, Frank Proske, Olena Tymoshenko. 2024-04-30. Fokker-Planck equation for McKean-Vlasov SPDEs driven by time-space Brownian sheet. https://arxiv.org/abs/2404.19490

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