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Around Tsirelson’s equation, or: the evolution process may not explain everything. (English) Zbl 1328.60170

Summary: We present a synthesis of a number of developments which have been made around the celebrated Tsirelson’s equation from [B. S. Tsirel’son, Theory Probab. Appl. 20, 416–418 (1975); translation from Teor. Veroyatn. Primen. 20, 427–430 (1975; Zbl 0353.60061)], 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 \(G=\mathbb{T}\).

MSC:

60J05 Discrete-time Markov processes on general state spaces
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60J50 Boundary theory for Markov processes
37H10 Generation, random and stochastic difference and differential equations

Citations:

Zbl 0353.60061
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References:

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