Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions

Hongxia Chu, Haiyan Yuan and Quanxin Zhu ()
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Hongxia Chu: School of Electrical and Information Engineering, Heilongjiang Institute of Technology, Harbin 150050, China
Haiyan Yuan: Department of Mathematics, Heilongjiang Institute of Technology, Harbin 150050, China
Quanxin Zhu: School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Mathematics, 2025, vol. 13, issue 15, 1-20

Abstract: This paper focuses on McKean-Vlasov stochastic differential equations under local Lipschitz conditions. We first introduce the stochastic interacting particle system and prove the propagation of chaos. Then we establish a truncated stochastic theta scheme to approximate the interacting particle system and obtain the strong convergence of the continuous-time truncated stochastic theta scheme to the non-interacting particle system. Furthermore, we study the asymptotical mean square stability of the interacting particle system and the truncated stochastic theta method. Finally, we give one numerical example to verify our theoretical results.

Keywords: McKean-Vlasov stochastic differential equation; Wasserstein distance; truncated stochastic theta method; strong convergence; asymptotical mean square stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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