By using Malliavin calculus, Bismut type formulas are established for the Lions derivative of , where 0, is a bounded measurable function, and solves a distribution dependent SDE with initial distribution . As applications, explicit estimates are derived for the Lions derivative and the total variational distance between distributions of solutions with different initial data. Both degenerate and non-degenerate situations are considered. Due to the lack of the semi-group property and the invalidity of the formula = , essential difficulties are overcome in the study.
Joint work with Professor Feng-Yu Wang
- Stochastic Analysis Seminar