RANDOM RECORD PROCESSES AND STATE-DEPENDENT THINNING

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:55

Article

BROWNE, S ; BUNGE, J

关键词: MIXED POISSON PROCESS;    PURE BIRTH PROCESS;    PASCAL PROCESS;    CHARACTERIZATION;    MITTAG-LEFFLER DISTRIBUTION;   

DOI  :  10.1016/0304-4149(94)00022-L

来源: Elsevier

【 摘 要 】

Suppose that a point process ($) over bar N-t = T-1, T-2,... on [0, infinity) is thinned by independently retaining T-n with probability p(n). Our main examples are the classical p-thinning (p(c) = p) and the random record process (p(n) = 1/n). When ($) over bar N-t is a mixed, nonhomogeneous Poisson process, we find conditions under which the thinned process is Poisson. When ($) over bar N-t is a pure birth process (gamma-mixed Poisson with exponential rate), we show that the record process is Markov renewal, with an interesting structure, and we compare this with related asymptotic results. When ($) over bar N-t is a Mittag-Leffler renewal process (the homogeneous Poisson is a special case), we give a ''Deheuvels-type'' representation of the record process (Deheuvels, 1982) and related characterization results.

【 授权许可】

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