# Colloquium: Tuesday, January 14, 2020. Speaker: Benjamin Weiss (HUJI). Title: “Deterministic processes and predictive sequences”.

Place: Room 614 in the Education & Sciences Building

Time: 14:00

Abstract:

A predictive sequence is a subset P of {n<0} such that for any finite valued zero entropy stationary ergodic process {X_j} the random variable X_0 is a function of {X_j : j \in P}. Examples of such sequences are sets of the form {n < 0 : n \alpha \in U} where U is a neighborhood of the identity in a compact abelian group K and \alpha is any element of K. I will discuss some necessary, and some sufficient conditions for a sequence to be predictive. Connections with an analogous notion for L^2 predictability of Gaussian processes will also be shown.

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