On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions.

In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownians motion is studied. The existence and uniqueness theorem of strong solutions for the distribution dependent stochastic differential equations is established. Then, sufficient conditions are provided to guarantee the solutions to be stable in several different senses in terms of Lyapunov function. Finally, we show that the solutions of the distribution dependent stochastic differential equations can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence. [ABSTRACT FROM AUTHOR]