Strong convergence of an explicit numerical approximation for n-dimensional superlinear SDEs with positive solutions

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Cai, Yongmei and Guo, Qian and Mao, Xuerong (2024) Strong convergence of an explicit numerical approximation for n-dimensional superlinear SDEs with positive solutions. Mathematics and Computers in Simulation, 216. pp. 198-212. ISSN 0378-4754 (https://doi.org/10.1016/j.matcom.2023.09.011)

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Abstract

For a stochastic differential equation (SDE) with a unique positive solution, a rational numerical method is expected to be structure preserving. However, most existing methods are not, as far as we know. Some characteristics of the SDE models including the multi-dimension and super-linearity make it even more challenging. In this work, we fill the gap by proposing an explicit numerical method which is not only structure preserving but also cost effective. The strong convergence framework is set up by moment convergence analysis. We use the Lotka–Volterra system to elaborate our theory, nevertheless, the method works for a wide range of multi-dimensional superlinear SDE models.

ORCID iDs

Cai, Yongmei, Guo, Qian and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:86966
    Dates:
    Date
    Event
    28 February 2024
    Published
    29 September 2023
    Published Online
    19 September 2023
    Accepted
    5 December 2022
    Submitted
    Notes:Copyright © Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:16 Oct 2023 12:12
    Last modified:12 Dec 2024 15:02
    URI:https://strathprints.strath.ac.uk/id/eprint/86966
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