Approximations of Mckean-Vlasov SDEs with Irregular Coefficients

2019/05/21 by Jianhai Bao, Xing Huang, Bao, Jianhai +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1905.08522

openalex publication_date 2019/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to approximate several kinds of \it Mckean-Vlasov SDEs with \it irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler-Maruyama scheme associated with the consequent weakly interacting particle systems are investigated for Mckean-Vlasov SDEs, where (i) the diffusion terms are Hölder continuous by taking advantage of Yamada-Watanabe's approximation approach and (ii) the drifts are Hölder continuous by freezing distributions followed by invoking Zvonkin's transformation trick.

Citations

• Strong well-posedness of McKean-Vlasov stochastic differential equation with Hölder drift
• Simulation of McKean Vlasov SDEs with super linear growth
• Distribution dependent SDEs for Landau type equations

Related

• Convergence analysis of an explicit method and its random batch approximation for the McKean-Vlasov equations with non-globally Lipschitz conditions
• On the convergence of the Euler-Maruyama scheme for McKean-Vlasov SDEs
• Well-posedness and propagation of chaos for jump-type McKean-Vlasov SDEs with irregular coefficients
• Volterra type McKean-Vlasov SDEs with singular kernels: Well-posedness, Propagation of Chaos and Euler schemes
• Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions