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On a New Shot Noise Process and the Induced Survival Model
- On a New Shot Noise Process and the Induced Survival Model
- Cha, Ji Hwan; Finkelstein, Maxim
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
- METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY vol. 20, no. 3, pp. 897 - 917
- Shot noise process; Poisson process; Generalized Polya process; Failure rate; History-dependent residual lifetime
- SCIE; SCOPUS
- Document Type
- 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.
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