Abstract
Abstract
Numerical analysis of stochastic delay differential equations has been widely developed but frequently for the cases where the delay term has a simple feature. In this paper, we aim to study a more general case of delay term which has not been much discussed so far. We mean the case where the delay term takes random values. For this purpose, a new continuous split-step scheme is introduced to approximate the solution and then convergence in the mean-square sense is investigated. Moreover, given a test equation, the mean-square asymptotic stability of the scheme is presented. Numerical examples are provided to further illustrate the obtained theoretical results.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference32 articles.
1. Akhtari, B., Babolian, E., Neuenkirch, A.: An Euler scheme for stochastic delay differential equations on unbounded domains: pathwise convergence. Discrete Contin. Dyn. Syst., Ser. B 20(1), 23–38 (2015)
2. Arthi, G., Park, J.H., Jung, H.Y.: Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay. Appl. Math. Comput. 248, 328–341 (2014)
3. Baker, C.T.H., Buckwar, E.: Numerical analysis of explicit one-step methods for stochastic delay differential equations. LMS J. Comput. Math. 3, 315–335 (2000)
4. Baker, C.T.H., Buckwar, E.: Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations. Comput. Appl. Math. 184, 404–427 (2005)
5. Chen, L., Wu, F.: Almost sure exponential stability of the backward Euler–Maruyama scheme for stochastic delay differential equations with monotone-type condition. J. Comput. Appl. Math. 282, 44–53 (2015)
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