Thursday, March 22
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: Benjamin Weiss
Affiliation: Hebrew University
Title: Universal estimators in probability and ergodic theory.
Abstract: A common paradigm for many investigations is the observer who gathers more and more data concerning a system and wishes to estimate various features of the system. In ergodic theory the system is often a measure preserving system (X, B, μ, T), and the "more and more data" is the evolving itinerary of a fixed starting point x∈X with respect to some finite partition P of X. In probability theory one formulates this situation as observing the first n outputs of a stationary stochastic process. Universal estimators are those which do not explicitly involve the system itself. I will describe some recent results connected with these ideas.