US-Finland Cooperative Research: Regeneration for Chains with Infinite Memory (Mathematics)

该奖项支持威斯康星大学麦迪逊分校的Peter Ney教授与芬兰赫尔辛基大学数学系的Esa Nummelin教授在数学方面的合作研究。他们合作的基础是在数学分析方面的互补技能、知识和技术的结合。多年来，他们在马尔可夫加性过程、大偏差理论和随机过程再生技术等领域进行了卓有成效的合作。他们目前的研究目标是为一类被称为“无限记忆链”的过程开发再生结构。这些模型在人口增长和统计物理等领域是有用的。一个随机过程的再生结构的存在是重要的，因为它使该过程的各种极限定律可及；例如，大数定律、中心极限定理和大偏差定理的适当表述版本。

This award supports Professor Peter Ney, University of Wisconsin, Madison, for collaborative research in mathematics with Professor Esa Nummelin of the Department of Mathematics, University of Helsinki, Finland. The basis of their cooperation is the joining of complementary skills, knowledge and techniques in mathematical analysis. They have collaborated very productively for several years in areas such as Markov Additive Processes, large deviation theory, and regeneration techniques for stochastic processes. The objective of their current research is to develop regeneration structures for a class of processes called "chains with infinite memory." These are useful as models in areas such as population growth and statistical physics. The existence of a regeneration structure for a stochastic process is important because it makes accessible a variety of limit laws for the process; for example, suitably formulated versions of laws of large numbers, central limit theorems and large deviation theorems.