## 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.