Conditional McKean–Vlasov differential equations with common poissonian noise: Propagation of chaos

A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean–Vlasov limits of such system are formulated studying first both systems individually. By letting the population size growing to infinite, the weak convergence of the solutions of such systems is proved. In other words, propagation of chaos of such systems is obtained.