Distribution Dependent SDEs with Singular Coefficients

Abstract

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient estimates and Harnack type inequalities are derived. These generalize the corresponding results derived for classical SDEs, and are new in the distribution dependent setting.

28pages

References in corpus (3)

• Ergodicity of stochastic differential equations with jumps and singular coefficients
• Nonlinear Fokker-Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs
• Mild Solutions and Harnack Inequality for Functional SPDEs with Dini Drift