Rough nonlocal diffusions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:141

Article

Coghi, Michele¹  Nilssen, Torstein² 

[1] TU Berlin, Str 17 Juni 136, D-10623 Berlin, Germany

[2] Univ Agder, Inst Math, Kristiansand S, Norway

关键词: Rough paths;    Stochastic PDEs;    McKean-Vlasov;    Non-local equations;   

DOI  :  10.1016/j.spa.2021.07.002

来源: Elsevier

【 摘 要 】

We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with common noise. To study the equation we build a self-contained framework of non-linear rough integration theory which we use to study McKean-Vlasov equations perturbed by rough paths. We construct an appropriate notion of solution of the corresponding Fokker-Planck equation and prove well-posedness. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free