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Positivity preserving truncated Euler–Maruyama Method for stochastic Lotka–Volterra competition model
Journal of Computational and Applied Mathematics ( IF 2.4 ) Pub Date : 2021-03-26 , DOI: 10.1016/j.cam.2021.113566
Xuerong Mao , Fengying Wei , Teerapot Wiriyakraikul

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.



中文翻译:

随机Lotka–Volterra竞争模型的保正性截断的Euler–Maruyama方法

著名的随机Lotka–Volterra模型在生态系统中相互作用多种物种,具有一些典型特征:高度非线性,正解和多维。已知的数值方法,包括应用到其上的驯服/截尾的Euler-Maruyama(EM),都不能保持其正值。本文的目的是修改截短的EM,以建立新的正保留截短的EM(PPTEM)。为了简化证明以及使我们的理论更容易理解,我们将首先开发一个非负保留的截短EM(NPTEM),然后建立PPTEM。当然,我们应该指出,NPTEM拥有自己的权利,因为应用程序中的许多SDE模型都有其非负解决方案。

更新日期:2021-04-05
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