Pascal processes and their characterization

F. T. Bruss and L. C. G. Rogers

Stochastic Processes and their Applications, 1991, vol. 37, issue 2, 331-338

Abstract: Let ([Pi]t) be a counting process on + with the property that for any t, T with 0[less-than-or-equals, slant]t[less-than-or-equals, slant]T the distribution of [Pi]T given the past t is Pascal (negative binomial) with one parameter being [Pi]t+1 and the probability parameter depending only on t and T. Does such a process exist? If so, how is it characterized? Finally, what is the most convenient way to model such a process? These questions are motivated by the distinguished role of the Pascal distribution in finding explicit solutions of optimal selection problems based on relative ranks. We answer them completely.

Keywords: Yule; processes; mixed; Poisson; processes; record; processes; martingales (search for similar items in EconPapers)
Date: 1991
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