# On the infinite time horizon approximation for L\'evy-driven McKean-Vlasov SDEs with common noise

## TL;DR

This paper proves the existence, uniqueness, and propagation of chaos for Le9vy-driven McKean-Vlasov SDEs with common noise over an infinite time horizon, advancing theoretical understanding of such stochastic systems.

## Contribution

It introduces a novel approach to establish solutions and analyze propagation of chaos for Le9vy-driven McKean-Vlasov SDEs with common noise on an infinite horizon.

## Key findings

- Existence and uniqueness of solutions established
- Propagation of chaos analyzed in the presence of common noise
- Method based on contraction mapping in probability measure space

## Abstract

In this work, we establish the existence and uniqueness of solutions to McKean-Vlasov stochastic differential equations (SDEs) driven by L\'evy 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 L\'evy-driven McKean-Vlasov SDEs in the presence of common noise.