Convergence and Stability of the Truncated Stochastic Theta Method for McKean-Vlasov Stochastic Differential Equations Under Local Lipschitz Conditions - Hongxia Chu; Haiyan Yuan; Quanxin Zhu (Mathematics)
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.