McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle

2025/08/04 by Yuhang Jiang, Jinming Li, Jiang, Yuhang +3
Economics, Econometrics and Finance · Mathematics · #60F10 #60H15 #Bounded function #Compact space #Discretization #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Kullback–Leibler divergence #Large deviations theory #Navier-Stokes equation solutions #Poisson distribution #Probability (math.PR) #Random field #Stochastic differential equation #Stochastic partial differential equation #Stochastic processes and financial applications #Variational principle

paper · pdf · doi:10.48550/arxiv.2508.02014

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of McKean-Vlasov stochastic partial differential equations with monotone coefficients. The main results can be applied to quasi-linear McKean-Vlasov equations such as distribution dependent stochastic porous media equation and stochastic p-Laplace equation. Our proof is based on the weak convergence approach introduced by Budhiraja et al. for Poisson random measures, the time discretization procedure and relative entropy estimates. In particular, we succeed in dropping the compactness assumption of embedding in the Gelfand triple in order to deal with the case of bounded and unbounded domains in applications.

Citations

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Related

• McKean-Vlasov SDE and SPDE with Locally Monotone Coefficients
• Large Deviation Principle for McKean-Vlasov Quasilinear Stochastic Evolution Equations
• Large deviation principle for a class of stochastic partial differential equations with fully local monotone coefficients perturbed by Lévy noise
• Large deviations for locally monotone stochastic partial differential equations driven by Lévy noise
• Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs