3/1/2006

Benjamin Weiss
Hebrew University of Jerusalem

On functions of stationary stochastic processes

I will discuss two kinds of results about functions of SSP. Both will involve sequences of functions $F_n(x_1^n)$ defined on the initial n varaibles of a SSP. The first concerns universal estimates for the number of upcrossings of the sequence $F_n$ leading to constructive versions of the classical limit theorems such as Doob's martingale convergence theorem, Birkhoff's ergodic theorem and  the Shannon-Mcmillan-Breiman theorem. The second kind will chaacterize when such sequences can converge to  isomorphism invariants of SSP.