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Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 897–917 | Cite as

On a New Shot Noise Process and the Induced Survival Model

  • Ji Hwan Cha
  • Maxim Finkelstein
Article

Abstract

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.

Keywords

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

Mathematics Subject Classification (2010)

60K10 62P30 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of StatisticsEwha Womans UniversitySeoulKorea
  2. 2.Department of Mathematical StatisticsUniversity of the Free StateBloemfonteinSouth Africa
  3. 3.ITMO UniversitySt. PetersburgRussia

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