The classical bi-Poisson process: An invertible quadratic harness

Wlodzimierz Bryc and Jacek Wesolowski

Statistics & Probability Letters, 2006, vol. 76, issue 15, 1664-1674

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.

Keywords: Conditional; moments; Harnesses; Linear; birth; process; Linear; death; process (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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