This work concerns with the numerical approximation for the stochastic Lotka–Volterra model originally studied by Mao et al. (Stoch Process Appl 97(1):95–110, 2002). The natures of the model including multi-dimension, super-linearity of both the drift and diffusion coefficients and the positivity of the solution make most of the existing numerical methods fail. In particular, the super-linearity of the diffusion coefficient results in the explosion of the 1st moment of the analytical solution at a finite time. This becomes one of our main technical challenges. As a result, the convergence framework is to be set up under the \(\theta \)th moment with \(0<\theta <1\). The idea developed in this paper will not only be able to cope with the stochastic Lotka–Volterra model but also work for a large class of multi-dimensional super-linear SDE models.

这项工作涉及最初由 Mao 等人研究的随机 Lotka-Volterra 模型的数值近似。(Stoch Process Appl 97(1):95–110, 2002)。模型的多维性、漂移系数和扩散系数的超线性以及解的正性等特性使得大多数现有的数值方法都失败了。特别地，扩散系数的超线性导致解析解的一阶矩在有限时间内爆炸。这成为我们的主要技术挑战之一。因此，收敛框架将在\(\theta \)时刻下建立，其中\(0<\theta <1\). 本文提出的想法不仅能够处理随机 Lotka–Volterra 模型，而且适用于一大类多维超线性 SDE 模型。