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.
