Convergence analysis of an explicit method and its random batch approximation for the McKean-Vlasov equations with non-globally Lipschitz conditions

2023/05/29 by Qian Guo, Jie He, Guo, Qian +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2305.18054

openalex publication_date 2023/05/29 · openalex created_date 2023/05/31 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion coefficients. We establish a propagation of chaos result, based on which the McKean-Vlasov equation is approximated by an interacting particle system. A truncated Euler scheme is then proposed for the interacting particle system allowing for a Khasminskii-type condition on the coefficients. To reduce the computational cost, the random batch approximation proposed in [Jin et al., J. Comput. Phys., 400(1), 2020] is extended to the interacting particle system where the interaction could take place in the diffusion term. An almost half order of convergence is proved in L^p sense. Numerical tests are performed to verify the theoretical results.

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• Strong error analysis and first-order convergence of Milstein-type schemes for McKean-Vlasov SDEs with superlinear coefficients
• Euler-type methods for Levy-driven McKean-Vlasov SDEs with super-linear coefficients: mean-square error analysis

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