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- Title
Continuous Dependence for Stochastic Functional Differential Equations with State-Dependent Regime-Switching on Initial Values.
- Authors
Shao, Jing Hai; Zhao, Kun
- Abstract
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.
- Subjects
STOCHASTIC differential equations; DEPENDENCE (Statistics); JUMP processes; EULER method; FUNCTIONAL differential equations
- Publication
Acta Mathematica Sinica, 2021, Vol 37, Issue 3, p389
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-020-9205-8