Random walks and branching processes in random environments under Spitzer's condition

斯皮策条件下随机环境中的随机游走和分支过程

• 批准号: EP/D064988/1
• 负责人: Andreas Kyprianou
• 金额: $ 2.03万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD064988%2F1
• 关键词: Random; walks; branching; processes; random

Random walks and branching processes form two fundamental cornerstones of the theory ofstochastic processes. The first models the evolution of a randomly moving particle in discrete time and the second (in its most basic form) modelsthe evolution in discrete time of an asexually reproducing population.There are many intimate relationships between these two classes of processes. In particular via path transformations and/or limit theorems.This makes them very attractive mathematical objects in which the interactive phenomena that occur between them has often provided a platform for the development of much deeper and generic mathematical objects of study which themselves lead on to a number of mathematical applications. The current proposal aims at funding a two month visit of one of the leading experts in the field of branching processes, Prof. V. Vatutin, with a view to two main objectives.1. Establishing new results concerning random walks whose probabilistic transitions are governed by a mathematical mechanism whichitself is randomised (the so called random walk in random environment) by drawing conclusions frombranching processes in random environments and vice versa.2. In light of the creation of the new Maxwell Institute for Mathematical Sciences, Prof. Vatutin will give a special lecture course on modern aspects of classical branching processes (including branching processes in random environment and application of branching processes to study queueing systems and some problems inpopulation biology).

随机游动和分枝过程构成了随机过程理论的两个基本基石。第一类模拟离散时间内随机运动粒子的演化，第二类(以其最基本的形式)模拟离散时间内无性繁殖种群的演化。这两类过程之间有许多密切的关系。特别是通过路径变换和/或极限定理。这使得它们成为非常吸引人的数学对象，其中在它们之间发生的交互现象通常为开发更深层次和更一般的数学研究对象提供了平台，这些研究对象本身导致了许多数学应用。目前的提议旨在资助分支程序领域的一位主要专家V.Vatutin教授进行为期两个月的访问，以期实现两个主要目标1。通过从随机环境中的分支过程得出结论，建立关于随机行走的新结果，该随机行走的概率转变由一种数学机制管理，该数学机制本身是随机化的(随机环境中的所谓的随机行走)，反之亦然。鉴于麦克斯韦数学科学研究所的成立，Vatutin教授将就经典分支过程的现代方面(包括随机环境中的分支过程以及分支过程在研究排队系统和种群生物学中的一些问题的应用)进行专题讲座。