An advanced numerical scheme for multi-dimensional stochastic Kolmogorov equations with superlinear coefficients

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Cai, Yongmei and Mao, Xuerong and Wei, Fengying (2024) An advanced numerical scheme for multi-dimensional stochastic Kolmogorov equations with superlinear coefficients. Journal of Computational and Applied Mathematics, 437. 115472. ISSN 0377-0427 (https://doi.org/10.1016/j.cam.2023.115472)

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Abstract

This work develops a novel approximation for a class of superlinear stochastic Kolmogorov equations with positive global solutions. On the one hand, most existing explicit methods that work for the superlinear stochastic differential equations (SDEs), e.g. various modified Euler-Maruyama (EM) methods, fail to preserve positivity of the solution. On the other hand, methods that preserve positivity are mostly implicit, or fail to cope with the multi-dimensional scenario. This work aims to construct an advanced numerical method which is not only naturally structure preserving but also cost effective. A strong convergence framework is then developed with an almost optimal convergence rate of order arbitrarily close to 1=2. To make the arguments concise, we elaborate our theory with the generalised stochastic Lotka-Volterra model, though the method is applicable to a wide bunch of multi-dimensional superlinear stochastic Kolmogorov systems in various fields including finance and epidemiology.

ORCID iDs

Cai, Yongmei, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864 and Wei, Fengying;
  • Item type:Article
    ID code:86448
    Dates:
    Date
    Event
    29 February 2024
    Published
    6 August 2023
    Published Online
    26 July 2023
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:11 Aug 2023 12:56
    Last modified:12 Dec 2024 14:55
    URI:https://strathprints.strath.ac.uk/id/eprint/86448
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