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 logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:63360
    Dates:
    Date
    Event
    28 February 2019
    Published
    18 February 2018
    Accepted
    Notes: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:11 Nov 2024 11:55
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/63360
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