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The classical bi-Poisson process: An invertible quadratic harness

Author

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  • Bryc, Wlodzimierz
  • Wesolowski, Jacek

Abstract

We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in Bryc and Wesolowski [2005. Conditional moments of q-Meixner processes. Probab. Theory Related Fields 131, 415-441 ], Bryc et al. [2005b. Quadratic harnesses, q-commutations, and orthogonal martingale polynomials. Trans. Amer. Math. Soc. , to appear], and Bryc et al. [2005a. The bi-Poisson process: a quadratic harness ]. It can be constructed from a pair of independent Poisson processes with the same gamma-distributed intensity.

Suggested Citation

  • Bryc, Wlodzimierz & Wesolowski, Jacek, 2006. "The classical bi-Poisson process: An invertible quadratic harness," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1664-1674, September.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:15:p:1664-1674
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    References listed on IDEAS

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    1. Gut, Allan & Janson, Svante, 2001. "Tightness and weak convergence for jump processes," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 101-107, March.
    2. Mansuy, Roger & Yor, Marc, 2005. "Harnesses, Lévy bridges and Monsieur Jourdain," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 329-338, February.
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    Cited by:

    1. Matysiak, Wojciech & Świeca, Marcin, 2015. "Zonal polynomials and a multidimensional quantum Bessel process," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3430-3457.
    2. Wojciech Matysiak, 2017. "Hypergroups and Quantum Bessel Processes of Non-integer Dimensions," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1677-1691, December.

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