Stochastic functional Kolmogorov equations II: Extinction
Stochastic functional Kolmogorov equations II: Extinction
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DOI：
10.1016/j.jde.2021.05.043
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发表时间：
2021-05
影响因子：
2.4
通讯作者：
D. Nguyen;N. Nguyen;G. Yin
中科院分区：
文献类型：
--
作者：
D. Nguyen;N. Nguyen;G. Yin
这项工作，第二部分，和它的同伴第一部分一起发展了随机泛函Kolmogorov方程的一个新的框架，它是依赖于当前状态和过去状态的非线性随机微分方程。由于问题的复杂性，将我们的贡献分为两部分来回答生物学和生态学中的一个长期存在的问题是很自然的。一个种群长期存在和灭绝的最低条件是什么？我们工作的第一部分提供了对持久性的描述，而在这一部分中，灭绝是主要的焦点。本文所使用的技术是新发展的泛函ITOHORM公式和动态系统方法的结合。与无时滞随机Kolmogorov系统的研究相比，主要的困难在于必须处理无限维系统。在考察了随机占领措施和考察了边界附近功能系统的行为之后，描述了灭绝的特征。当不存在过去的依赖关系时，我们对系统的长期行为的刻画立即退化为Kolmogorov系统的刻画。还审查了一些申请。
This work, Part II, together with its companion-Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past states. Because of the complexity of the problems, it is natural to divide our contributions into two parts to answer a long-standing question in biology and ecology. What are the minimal conditions for long-term persistence and extinction of a population? Part I of our work provides characterization of persistence, whereas in this part, extinction is the main focus. The techniques used in this paper are combination of the newly developed functional Itô formula and a dynamic system approach. Compared to the study of stochastic Kolmogorov systems without delays, the main difficulty is that infinite dimensional systems have to be treated. The extinction is characterized after investigating random occupation measures and examining behavior of functional systems around boundaries. Our characterizations of long-term behavior of the systems reduce to that of Kolmogorov systems without delay when there is no past dependence. A number of applications are also examined.