On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with common noise

In this work, we establish the existence and uniqueness of solutions to McKean-Vlasov stochastic differential equations (SDEs) driven by Lévy processes with common noise on an infinite time horizon, by means of a contraction mapping principle in the space of probability measures. In addition, we analyse the propagation of chaos for Lévy-driven McKean-Vlasov SDEs in the presence of common noise.