## B. Tsirelson | ## Innovation | ## Recent works |

"Within and beyond the reach of Brownian innovation."

Proc. Internat. Congress Math. (Berlin 1998), Vol. 3, 311-320.

Available online (free of charge, thanks to Documenta Mathematica):

www.mathematik.uni-bielefeld.de/documenta/xvol-icm/12/Tsirelson.MAN.html

A short (10 pages) survey of old and recent results of ergodists and probabilists: Barlow, Beghdadi-Sakrani, Dubins, Émery, Feldman, Heicklen, Hoffman, Knight, Le Gall, Schachermayer, Smorodinsky, Song, Stepin, Tsirelson, Vershik, Warren, Yor. Bibl. 44 refs.

Given a system whose time evolution is random, we often try to describe it as a deterministic system under independent random influences. Doing so, we reduce complicated statistical correlations to a complicated but deterministic mechanism, and a stochastic but uncorrelated noise. That is the idea of innovation. The corresponding mathematics is surprisingly interesting.

- The name of the game.
- Trivial cases.
- Decreasing sequences are highly non-trivial.
- Cosiness.
- Applications to continuous time.
- From stochastic analysis to stochastic topology.
- White noise versus black noise.

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