Von Mises statistics for a measure preserving transformation
Feb 28 2013 – 3:00pm – 4:00 pm
Manfred Denker (The Pennsylvania State University)
Let T be a measure preserving transformation on a probability space. I will present three theorems on the almost sure and weak convergence of sums of the form
The difficulty here arises from the fact that the summands are not well defined as random variables on the probability space. Therefore I will explain how to describe reasonable subspaces of L2 where these variables can be defined a.s.
As a result I will state new ergodic theorems and new central limit theorems obtained from a suitable martingale approximation in the sense of Gordin’s 1968 paper.