Good Functions and Bad Functions, Moving Averages and Coboundaries

Professor Joseph Rosenblatt, Indiana University-Purdue University Indianapolis and University of Illinois at Urbana-Champaign. Part of the Analysis and Applications Seminar Series.

We study the local behavior of the convergence of classes C of stochastic processes that employ a measure-preserving transformation τ and are defined on spaces of measurable functions f. Local behavior means considering these questions:

  1. Given τ, for which f is there a.e. boundedness or even a.e. convergence for a stochastic process in C?
  2. Given f, for which τ is there is a.e. boundedness or even a.e. convergence for a stochastic process in C?