Von Mises statistics for a measure preserving transformation
Time
Feb 28 2013 – 3:00pm – 4:00 pm
Location
MW154
Speaker
Manfred Denker (The Pennsylvania State University)
Abstract
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
∑0≤ik<n,k=1,…,dh(Ti1,…,h(Tid).
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.