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A case of discrete chaotic representation. (Un cas de représentation chaotique discrète.) (French) Zbl 0738.60066

Séminaire de probabilités XXIII, Lect. Notes Math. 1372, 146 (1989).
[For the entire collection see Zbl 0722.00030.]
A family of orthogonal martingales, associated to a discrete finite Markov chain with strictly positive transition probabilities is constructed, which forms a basis in the \(L^ 2\)-space asssociated with the chain. This fact is interpreted in the way that any such finite Markov chain can be realized as a “quantum diffusion” in the sense of Evans-Hudson on a “toy” Fock space of appropriate dimension.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)

Citations:

Zbl 0722.00030
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