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 Probability Surveys > Vol. 12 (2015) open journal systems 


Around Tsirelson's equation, or: The evolution process may not explain everything

Kouji Yano, Kyoto University
Marc Yor, Université Paris VI


Abstract
We present a synthesis of a number of developments which have been made around the celebrated Tsirelson's equation (1975), conveniently modified in the framework of a Markov chain taking values in a compact group \(G\), and indexed by negative time. To illustrate, we discuss in detail the case of the one-dimensional torus \(G=\mathbb{T}\).

AMS 2000 subject classifications: Primary 60J05; secondary 60B15, 60J50, 37H10.

Keywords: Tsirelson's equation, evolution process, extremal points, strong solution, uniqueness in law.

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Yano, Kouji, Yor, Marc, Around Tsirelson's equation, or: The evolution process may not explain everything, Probability Surveys, 12, (2015), 1-12 (electronic). DOI: 10.1214/15-PS256.

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Probability Surveys. ISSN: 1549-5787