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

该奖项支持威斯康星州大学的Peter Ney教授， 麦迪逊，数学合作研究与教授 埃萨Nummelin的数学系，大学 芬兰，赫尔辛基。 他们合作的基础是加入 数学中的互补技能、知识和技术 分析. 几年来， 在马尔可夫加性过程、大偏差等领域的年 随机过程理论和再生技术。 他们目前研究的目标是发展再生 结构的一类过程称为“链与无限 记忆“这些在人口等领域作为模型是有用的 增长和统计物理学。 再生的存在 随机过程的结构很重要，因为它使 可访问该过程的各种极限定律;例如， 大数定律的适当表述版本，中央 极限定理和大偏差定理。

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.