Fock space realizations of some classical Markov processes

• Autorzy: Bryc W. , Ejsmont W.
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Markov processes; non-commutative probability; bi-Poisson processes

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 301--313
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Bryc W.

• Department of Mathematics, University of Cincinnati, Cincinnati, OH 45221-0025, USA

autor

Ejsmont W.

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
• Department of Mathematics and Cybernetics, University of Economics, ul. Komandorska 118/120, 53-345 Wrocław, Poland

Bibliografia

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• [13] W. Bryc, W. Matysiak, and J. Wesołowski, The bi-Poisson process: a quadratic harness, Ann. Probab. 36 (2008), pp. 623-646. arxiv.org/abs/math.PR/0510208.
• [14] W. Bryc and J. Wesołowski, Bi-Poisson process, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10 (2007), pp. 277-291. arxiv.org/abs/math.PR/0404241.
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• [16] W. Ejsmont, Noncommutative characterization of free Meixner processes, Electron. Comm. Probab. 18 (12) (2013), pp. 1-12.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).