An N-dimensional lottery model for competition among $N\ge 2$ ecological species in stochastic environments is studied under the i.i.d. assumption. First, a system of nonlinear stochastic differential equations (SDEs) is developed as the diffusion approximation for the discrete lottery model. Then the existence and uniqueness of positive and bounded global solutions, as well as long-term dynamics for the solution are investigated. In particular, sufficient conditions under which extinction and persistence occur are constructed, respectively.

中文翻译：

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随机环境中多物种彩票竞争模型的动力学

一种N维抽签模型，用于相互竞争$否\ge \mathrm{2个}$在独立同分布假设下研究随机环境中的生态物种。首先，开发了一个非线性随机微分方程 (SDE) 系统作为离散彩票模型的扩散近似。然后研究了正的和有界的全局解的存在性和唯一性，以及解的长期动态。特别地，分别构造了发生灭绝和持续存在的充分条件。