McKean-Vlasov SDEs with Drifts Discontinuous under Wasserstein Distance

Abstract

Existence and uniqueness are proved for Mckean-Vlasov type distribution dependent SDEs with singular drifts satisfying an integrability condition in space variable and the Lipschitz condition in distribution variable with respect to $W_0$ or $W_0+W_{\theta }$ for some $\theta \ge 1$, where $W_0$ is the total variation distance and $W_{\theta }$ is the $L^{\theta }$-Wasserstein distance. This improves some existing results where the drift is either locally bounded in the space variable or continuous in the distribution variable with respect to the Wasserstein distance.

14 pages

References in corpus (2)

• Existence and Regularity of Solutions to Multi-Dimensional Mean-Field Stochastic Differential Equations with Irregular Drift
• A Zvonkin's transformation for stochastic differential equations with singular drift and related applications

Cited by in corpus (2)

• Exponential Convergence in Entropy and Wasserstein Distance for McKean-Vlasov SDEs
• Exponential Ergodicity for Non-Dissipative McKean-Vlasov SDEs