On a New Shot Noise Process and the Induced Survival Model

Ji Hwan Cha, Maxim Finkelstein

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3 Scopus citations


Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock process) is the homogeneous (or nonhomogeneous) Poisson process. However, most of the real life shock processes do not possess the independent increments property and the Poisson assumption is made just for simplicity. Recently, in the literature, a new point process, the generalized Polya process (GPP), has been proposed and characterized. The GPP is defined via the stochastic intensity that depends on the number of events in the previous interval and, therefore, does not possess the independent increments property. In this paper, we consider the GPP as an underlying shock process for the shot noise process. The corresponding survival model is considered and the survival probability and its failure rate are derived and thoroughly analyzed. Furthermore, a new concept, the history-dependent residual life time, is defined and discussed.

Original languageEnglish
Pages (from-to)897-917
Number of pages21
JournalMethodology and Computing in Applied Probability
Issue number3
StatePublished - 1 Sep 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.


  • Failure rate
  • Generalized Polya process
  • History-dependent residual lifetime
  • Poisson process
  • Shot noise process


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