An adaptive Euler-Maruyama scheme for McKean-Vlasov SDEs with super-linear growth and application to the mean-field FitzHugh-Nagumo model

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:400

Article

Reisinger, Christoph¹  Stockinger, Wolfgang¹ 

[1] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

关键词: McKean-Vlasov equations;    Interacting particle systems;    Strong solutions;    Numerical schemes for SDEs;   

DOI  :  10.1016/j.cam.2021.113725

来源: Elsevier

【 摘 要 】

In this paper, we introduce fully implementable, adaptive Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz continuity in the state variable for either, while global Lipschitz continuity is required for the measure component. We prove moment stability of the discretised processes and a strong convergence rate of 1/2. Several numerical examples, centred around a mean field model for FitzHugh-Nagumo neurons, illustrate that the standard uniform scheme fails and that the adaptive approach shows in most cases superior performance to tamed approximation schemes. In addition, we introduce and analyse an adaptive Milstein scheme for a certain sub-class of McKean-Vlasov SDEs with linear measure-dependence of the drift. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free