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

TL;DR

This paper studies complex stochastic differential equations with jumps and regime-switching, proving well-posedness, propagation of chaos, and an averaging principle for systems with multiple time scales.

Contribution

It introduces new results on the well-posedness and propagation of chaos for conditional McKean-Vlasov SDEs with jumps and regime-switching, including an averaging principle.

Findings

Established strong well-posedness using L2-Wasserstein distance.

Proved propagation of chaos with explicit convergence rate.

Developed an averaging principle for two time-scale equations.

Abstract

We investigate the conditional McKean-Vlasov stochastic differential equations with jumps and Markovian regime-switching. We establish the strong wellposedness using L2-Wasser-stein distance on the Wasserstein space. 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.