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

2025/08/28 by Ke Xu, Xu, Ke, Fen-Fen Yang +3
Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Financial Markets and Investment Strategies #Fluid Dynamics and Turbulent Flows #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2508.20807

openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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Related

• Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
• On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients
• Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise
• Long time behavior of one-dimensional McKean-Vlasov SDEs with common noise
• The ergodicity of nonlinear McKean-Vlasov stochastic differential equations with common noise