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.
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Supported in part by NNSFs of China (Grant Nos. 11771327, 11431014, 11831014)
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Shao, J.H., Zhao, K. Continuous Dependence for Stochastic Functional Differential Equations with State-Dependent Regime-Switching on Initial Values. Acta. Math. Sin.-English Ser. 37, 389–407 (2021). https://doi.org/10.1007/s10114-020-9205-8
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DOI: https://doi.org/10.1007/s10114-020-9205-8