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

Meyer, P. A.

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.

Reviewer: A.S.Holevo (Moskva)

MSC:

60J10

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

Keywords:

Wiener’s chaos; orthogonal martingales; finite Markov chain; quantum diffusion; Fock space

Citations:

Zbl 0722.00030