B. Tsirelson


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):

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.

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