On Distribution depend SDEs with singular drifts

Guohuan Zhao

Published 2020-03-10Version 1

We investigate the well-posedness of distribution dependent SDEs with singular coefficients. Existence is proved when the diffusion coefficient satisfies some non-degeneracy and mild regularity assumptions, and the drift coefficient satisfies an integrability condition in spatiotemporal variables and a continuity condition in the third variable with respect to the total variation distance. Uniqueness is also obtained under some additional Lipschitz type continuity assumptions in the distribution variable.