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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 33, Fasc. 2,
pages 301 - 313
 

FOCK SPACE REALIZATIONS OF SOME CLASSICAL MARKOV PROCESSES

Włodzimierz Bryc
Wiktor Ejsmont

Abstract: 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].

2000 AMS Mathematics Subject Classification: Primary: 46L54; Secondary: 46L53.

Keywords and phrases: Markov processes, non-commutative probability, bi-Poisson processes.

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