Probability Surveys

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

Kouji Yano and Marc Yor

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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 $G=\mathbb{T}$.

Article information

Source
Probab. Surveys, Volume 12 (2015), 1-12.

Dates
Received: January 2015
First available in Project Euclid: 21 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.ps/1437497795

Digital Object Identifier
doi:10.1214/15-PS256

Mathematical Reviews number (MathSciNet)
MR3374628

Zentralblatt MATH identifier
1328.60170

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60J50: Boundary theory 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]

Keywords
Tsirelson’s equation evolution process extremal points strong solution uniqueness in law

Citation

Yano, Kouji; Yor, Marc. Around Tsirelson’s equation, or: The evolution process may not explain everything. Probab. Surveys 12 (2015), 1--12. doi:10.1214/15-PS256. https://projecteuclid.org/euclid.ps/1437497795


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References

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