Well-posedness and Regularity for Distribution Dependent SPDEs with Singular Drifts

2020/02/25 by Xing Huang, Huang, Xing, Yulin Song +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2002.10617

Abstract

In this paper, the distribution dependent stochastic differential equation in a separable Hilbert space with a Dini continuous drift is investigated. The existence and uniqueness of weak and strong solutions are obtained. Moreover, some regularity results as well as gradient estimates and log-Harnack inequality are derived for the associated semigroup. In addition, dimensional free Harnack inequality with power and shift Harnack inequality are also proved when the noise is additive. All of the results extend the ones in the distribution independent situation.

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