由截尾稳定过程驱动的种群模型

A Population Model Driven by Truncated Stable Process

本文主要研究了由截尾α-稳定过程驱动的种群模型。在本文中我们首先限制稳定过程的跳跃高度,然后在一些假设下,证明带负跳的种群模型的全局正解仍然存在;同时我们利用Khasminskii引理及Lyapunov函数得到了该模型满足平稳分布和指数遍历的条件。此外,我们还给出了当α-4σαCα/9(2-α)<0时,该模型将趋于灭绝。

In this paper, we study the population model driven by truncated α-stable process. First, we limit the jump height of the stable process, and then under some assumptions, we prove that the global positive solution of the population model with negative jump still exists. At the same time, by using Khasminskii lemma and Lyapunov function, we obtain the conditions that the model satisfies the stationary distribution and exponential ergodicity. Besides, when&#160;α-4σαCα/9(2-α)<0, this model will go extinct.