Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation
Mao, Wei and Hu, Liangjian and Mao, Xuerong (2019) Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation. Discrete and Continuous Dynamical Systems - Series B, 24 (2). pp. 587-613. ISSN 1531-3492 (https://doi.org/10.3934/dcdsb.2018198)
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Abstract
In this paper, we are concerned with the asymptotic properties and numerical analysis of the solution to hybrid stochastic differential equations with jumps. Applying the theory of M-matrices, we will study the pth moment asymptotic boundedness and stability of the solution. Under the non-linear growth condition, we also show the convergence in probability of the Euler-Maruyama approximate solution to the true solution. Finally, some examples are provided to illustrate our new results.
ORCID iDs
Mao, Wei, Hu, Liangjian and Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864;-
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Item type: Article ID code: 63360 Dates: DateEvent28 February 2019Published18 February 2018AcceptedNotes: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version Mao, W, Hu, L & Mao, X 2018, 'Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation' Discrete and Continuous Dynamical Systems - Series B, pp. 1-33. is available online at: http://aimsciences.org/journals/home.jsp?journalID=2 Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 21 Feb 2018 14:37 Last modified: 04 Oct 2024 00:28 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/63360