Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: wellposedness, propagation of chaos, averaging principle (Q6198302)

The authors investigate the conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching. The \(L^2\)-Wasserstein distance is used to measure the regularity of the coefficients in the probability measure argument. The propagation of chaos is established for the associated mean-field interaction particle system with common noise and an explicit bound is provided on the convergence rate. The authors establish averaging principles for two time-scale conditional McKean-Vlasov equations, where much attention is paid to the convergence of the conditional distribution term.