Positivity preserving truncated Euler-Maruyama Method for stochastic Lotka-Volterra competition model

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:394

Article

Mao, Xuerong¹  Wei, Fengying²  Wiriyakraikul, Teerapot¹ 

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[2] Fuzhou Univ, Dept Math, Fuzhou, Fujian, Peoples R China

关键词: Stochastic differential equation;    Lotka-Volterra competition model;    Positivity preserving truncated;    Euler-Maruyama method;    Strong convergence;   

DOI  :  10.1016/j.cam.2021.113566

来源: Elsevier

【 摘 要 】

The well-known stochastic Lotka-Volterra model for interacting multi-species in ecology has some typical features: highly nonlinear, positive solution and multi-dimensional. The known numerical methods including the tamed/truncated Euler-Maruyama (EM) applied to it do not preserve its positivity. The aim of this paper is to modify the truncated EM to establish a new positive preserving truncated EM (PPTEM). To simplify the proof as well as to make our theory more understandable, we will first develop a nonnegative preserving truncated EM (NPTEM) and then establish the PPTEM. Of course, we should point out that the NPTEM has its own right as many SDE models in applications have their nonnegative solutions. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free