Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method

Deng, Shounian and Fei, Chen and Fei, Weiyin and Mao, Xuerong (2019) Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method. Applied Mathematics Letters, 96. pp. 138-146. ISSN 0893-9659 (https://doi.org/10.1016/j.aml.2019.04.022)

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Abstract

Consider a stochastic differential delay equation driven by G-Brownian motion (G-SDDE) dx(t) = f(x(t), x(t − τ))dt + g(x(t), x(t − τ))dB(t) + h(x(t), x(t − τ))dhBi(t). Under the global Lipschitz condition for the G-SDDE, we show that the G-SDDE is exponentially stable in mean square if and only if for sufficiently small step size, the Euler-Maruyama (EM) method is exponentially stable in mean square. Thus, we can carry out careful numerical simulations to investigate the exponential stability of the underlying G-SDDE in practice, in the absence of an appropriate Lyapunov function. A numerical example is provided to illustrate our results.

ORCID iDs

Deng, Shounian, Fei, Chen, Fei, Weiyin and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:67663
    Dates:
    Date
    Event
    1 October 2019
    Published
    11 May 2019
    Published Online
    23 April 2019
    Accepted
    22 January 2019
    Submitted
    Notes:© 2019 Elsevier Ltd. Shounian Deng, Chen Fei, Weiyin Fei, Xuerong Mao, Stability equivalence between the stochastic differential delay equations driven by G-Brownian motion and the Euler–Maruyama method, Applied Mathematics Letters, Volume 96, 2019, Pages 138-146, https://doi.org/10.1016/j.aml.2019.04.022
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:01 May 2019 13:03
    Last modified:11 Nov 2024 12:17
    URI:https://strathprints.strath.ac.uk/id/eprint/67663
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