Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term

Cai, Yongmei and Hu, Junhao and Mao, Xuerong (2022) Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term. Applied Numerical Mathematics. ISSN 0168-9274

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Abstract

This work concerns about the numerical solution to the stochastic epidemic model proposed by Cai et al. [2]. The typical features of the model including the positivity and boundedness of the solution and the presence of the square-root diffusion term make this an interesting and challenging work. By modifying the classical Euler-Maruyama (EM) scheme, we generate a positivity and boundedness preserving numerical scheme, which is proved to have a strong convergence to the true solution over finite time intervals. We also demonstrate that the principle of this method is applicable to a bunch of popular stochastic differential equation (SDE) models, e.g. the mean-reverting square-root process, an important financial model, and the multi-dimensional SDE SIR epidemic model.

ORCID iDs

Cai, Yongmei, Hu, Junhao and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:81741
    Dates:
    Date
    Event
    4 August 2022
    Published
    4 August 2022
    Published Online
    30 July 2022
    Accepted
    Keywords:stochastic differential equation, square-root process, positivity and boundedness preserving numerical model, strong convergence, Mathematics, Mathematics(all)
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:05 Aug 2022 14:44
    Last modified:18 Jan 2023 11:39
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/81741
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