 Random record processes and state dependent thinningSid Browne and John Bunge Stochastic Processes and their Applications, 1995, vol. 55, issue 1, 131-142 Abstract: Suppose that a point process , ... if [0, [infinity]) is thinned by independently retaining Tn with probability pn. Our main examples are the classical p-thinning (pn [reverse not equivalent] p) and the random record process (pn = 1/n). When is a mixed, nonhomogeneous Poisson process, we find conditions under which the thinned process is Poisson. When 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 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. Keywords: Mixed; Poisson; process; Pure; birth; process; Pascal; process; Characterization; Mittag-Leffler; distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:55:y:1995:i:1:p:131-142 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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