Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations

Liu, Wei and Mao, Xuerong (2016) Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations. Numerical Algorithms. pp. 1-20. ISSN 1017-1398 (https://doi.org/10.1007/s11075-016-0162-3)

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Abstract

In this paper, the Euler–Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method.

ORCID iDs

Liu, Wei and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:56598
    Dates:
    Date
    Event
    9 June 2016
    Published
    9 June 2016
    Published Online
    3 June 2016
    Accepted
    Notes:The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-016-0162-3
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:03 Jun 2016 14:48
    Last modified:11 Nov 2024 11:26
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/56598
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