Ron Peled (TAU)

will speak

Restoring topology from shifts (and application to stationary stochastic processes)

Abstract:

It is known that the topology of a Polish group is uniquely determined by it's Borel structure and group operations, but not in an explicit way. We expand on this theorem by giving a criterion for a given measurable function to be continuous by examining only it's shifts as functions on an abstract set. We show that the function is continuous iff there exists some separable metric which makes these shifts continuous. Using this, We continue to give a first proof of a similar criterion guessed by Tsirelson long ago for a stationary stochastic process to be sample continuous, the process is sample continuous iff some modification of it has continuous paths in some separable metric.

This work was done under the supervision of Prof. Boris Tsirelson. Many thanks are due also to Prof. A. Olevskii for proving a theorem which was the main ingredient in our first proof of the results. Later a simpler proof was found which will be presented in the lecture, but the research would never have started without Olevskii's contribution.

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Last update on 20/10/02.