Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: Wellposedness, propagation of chaos, averaging principle

Abstract

The conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching are investigated in this work. We use the L2-Wasserstein distance to measure the regularity of the coefficients in the probability measure argument. Also, we establish the propagation of chaos for the associated mean-field interaction particle system with common noise and provide an explicit bound on the convergence rate. Furthermore, an averaging principle is established for two time-scale conditional McKean-Vlasov equations, where much attention is paid to the convergence of the conditional distribution term.