McKean-Vlasov equations on infinite-dimensional Hilbert spaces with irregular drift and additive fractional noise

2019/12/16 by Martin Bauer, Bauer, Martin, Thilo Meyer‐Brandis +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Stability and Controllability of Differential Equations #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1912.07427

Abstract

This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here, McKean-Vlasov equations with additive noise are considered where the driving noise is cylindrical (fractional) Brownian motion. The existence and uniqueness of weak solutions are established for drift coefficients that are merely measurable, bounded, and continuous in the law variable. In particular, the drift coefficient is allowed to be singular in the spatial variable. Further, we discuss existence of a pathwisely unique strong solution as well as Malliavin differentiability.

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