Continuous Dependence for Stochastic Functional Differential Equations with State-Dependent Regime-Switching on Initial Values

作     者：Jing Hai SHAO Kun ZHAO Jing Hai SHAO;Kun ZHAO

作者机构：Center for Applied MathematicsTianjin UniversityTianjin 300072P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2021年第37卷第3期

页      面：389-407页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported in part by NNSFs of China(Grant Nos.11771327 11431014 11831014) 

主　　题：Regime-switching state-dependent Euler–Maruyama’s approximation 

摘      要：This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this problem is very different to the corresponding problem for SFDEs without switching or SFDEs with Markovian switching. We provide a method to overcome the intensive interaction between the continuous component and the discrete component based on a subtle application of Skorokhod’s representation for jumping processes. Furthermore, we establish the strong convergence of Euler–Maruyama’s approximations, and estimate the order of error. The continuous dependence on initial values of Euler–Maruyama’s approximations is also investigated in the end.