Hyperfinite Markov Processes

Seminar | February 8 | 3:10-4 p.m. | 1011 Evans Hall

 Haosui Duanmu, Haosui Duanmu, Department of Statistics, University of Toronto,

 Department of Statistics

I will start by giving a short introduction on Nonstandard Analysis and Nonstandard Probability Theory. I will then give then describe the basic idea of hyperfinite representations of probability spaces. A classical example of hyperfinite representation on unit inverval [0,1] with Lebesgue measure will be discussed. Then I will introduce the concept of Hyperfinite Markov processes. For standard Markov processes satisfying some moderate regularity conditions, we can construct a hyperfinite Markov process which has essentially the same transition probability as the standard processes. Such hyperfinite Markov processes also inherit many other properties from the original standard processes. We then establish the Markov Chain Ergodic Theorem under very general settings.