Alternative Approaches for the Transient Analysis of Markov Chains with Catastrophes
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In this paper we present various approaches for the transient analysis of a Markovian population process with total catastrophes. We discuss the pros and the cons of these methodologies and point out how they lead to different tractable extensions. As an illustrating example, we consider the nonhomogeneous Poisson process with total catastrophes. The extension of the probabilistic methodologies for analyzing models with binomial catastrophes is also discussed.
Key-wordsCatastrophes Disasters Non-homogeneous Poisson process Markov chain Renewal process Renewal equation Point process Order statistics property Backward recurrence time Age
AMS Subject Classification60J27 60J22
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