A note on the class of geometric counting processes

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

In this paper, we suggest a new class of counting processes, called the Class of Geometric Counting Processes (CGCP), where each member of the counting process in the class has increments described by the geometric distribution. Distinct from the Poisson process, they do not possess the property of independent increments, which usually complicates probabilistic analysis. The suggested CGCP is defined and the dependence structure shared by the members of the class is discussed. As examples of useful applications, we consider stochastic survival models under external shocks. We show that the corresponding survival probabilities under reasonable assumptions can be effectively described by the CGCP without specifying the dependence structure.

Original languageEnglish
Pages (from-to)177-185
Number of pages9
JournalProbability in the Engineering and Informational Sciences
Volume27
Issue number2
DOIs
StatePublished - Apr 2013

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