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

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.

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• Item metadata

  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 Apr 2024 02:19
  URI:	https://strathprints.strath.ac.uk/id/eprint/86448