HOROWITZ SEMINAR

PROBABILITY, ERGODIC THEORY and DYNAMICAL SYSTEMS

Benjamin Weiss (HUJI)

will speak

On the limit laws for the averages of stationary ergodic processes

ABSTRACT:
For iid random variables {X_i} it is a classical problem to determine the possible limiting distributions
of averages of the form S_n/a_n (where S_n is the sum of the first n of the X_i).

I will discuss what happens when one replaces the iid assumption by ergodic stationary.

Here is a sample result:

For any probability distribution F on R
there is a stationary ergodic process {X_i} such that
S_n/n converges in distribution to F

- and moreover such a process can defined over an arbitrary non-periodic ergodic system.

(joint work with Jean-Paul Thouvenot)

To suggest a talk (yours, or someone elses), contact Jon. Aaronson: aaro at post dot tau dot ac dot il

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