Stochastic processes with spatial constraints

具有空间约束的随机过程

• 批准号: 1007823
• 负责人: Nevena Maric
• 金额: $ 12万
• 依托单位: University of Missouri-Saint Louis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007823&HistoricalAwards=false
• 关键词: Stochastic; processes; spatial; constraints

The proposal focuses on infinite stochastic systems whose evolution is spatially constrained. It involves research on space-time inhomogeneous contact processes and branching random walks. It also involves a study of quasi-stationary distribution which is an essential concept related to equilibrium properties of a process conditioned to stay inside a sub-state-space. In an earlier work, we established a relation between quasi-stationary distributions and a Fleming-Viot particle system, which promises a novel, constructive and useful approach to quasi-stationarity. The proposed research on the subject will build on and significantly extend this work. Many natural and social phenomena arise as a result of interaction of large number of components (particles, humans, viruses, plants,...). Due to immense complexity of these systems, in order to make them more accessible, one assigns random components to these interactions and studies corresponding stochastic models. As suitable models for various physical systems, interacting stochastic systems have been studied extensively over the last decades. They were found also to be very useful models in epidemiology. The proposed project is related to infinite stochastic systems whose evolution is spatially constrained. Some mathematical questions to be addressed can be translated as:What happens with an infection if it spreads using only a certain number of individuals and contacts among them? How does reduction of a habitat affect distributions of a plant species? Beside its mathematical significance, the proposed research has very important applications in biogeography and evolution theory and hopefully it will generate fruitful collaborative interdisciplinary research.

该方案着眼于无限随机系统，其演化是空间受限的。它涉及到时空非均匀接触过程和分支随机游走的研究。它还涉及到准平稳分布的研究，这是一个与条件停留在子状态空间内的过程的平衡性质有关的基本概念。在以前的工作中，我们建立了准平稳分布与Fleming-Viot粒子系统之间的关系，这为研究准平稳提供了一种新的、有建设性的和有用的方法。关于这一主题的拟议研究将以这项工作为基础，并大大扩展这项工作。许多自然和社会现象是大量成分(粒子、人类、病毒、植物等)相互作用的结果。由于这些系统的巨大复杂性，为了使它们更容易被访问，人们为这些相互作用分配随机分量并研究相应的随机模型。交互随机系统作为一种适用于各种物理系统的模型，在过去的几十年里得到了广泛的研究。他们也被发现是流行病学中非常有用的模型。所提出的方案与无限随机系统有关，其演化是空间受限的。一些需要解决的数学问题可以解释为：如果感染只通过一定数量的个人和其中的接触者传播，会发生什么？栖息地的减少如何影响植物物种的分布？除了它的数学意义外，这项研究在生物地理学和进化论中也有非常重要的应用，并有望产生卓有成效的跨学科协作研究。