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Fock space realizations of some classical Markov processes

Bryc W., Ejsmont W.

Probability and Mathematical Statistics

2013

Vol. 33, Fasc. 2

301--313

We define a pair of non-commutative processes on a perturbed Fock space. Both processes have the same univariate distributions and satisfy a weak form of the polynomial martingale property. The processes give two non-equivalent Fock-space realizations of the same classical Markov process: the two-parameter bi-Poisson processes introduced in [12], and constructed in [13].