The Solidarity of Markov Renewal Processes

Ronald Pyke
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Ronald Pyke: University of Washington

Chapter Chapter 1 in Semi-Markov Models and Applications, 1999, pp 3-21 from Springer

Abstract: Abstract It is known that for a wide class of irreducible recurrent Markov Chains and Markov Renewal processes, the finiteness of the p-th moment of recurrence times is finite for one state if and only if it is finite for all states. This result also holds for a wide class of functional of the processes between successive occurrence times. Such results are known as solidarity theorems. In this paper, a solidarity theorem is proved concerning the property of “being in the domain of attraction of a stable law with specified parameters.” A basic identity linking additive random functions determined by two distinct states is emphasized, and used to derive solidarity results for moments and for the WLLN.

Keywords: Markov renewal processes; semi-Markov processes; solidarity theorems; moments; Teugel’s identity; domains of attraction; stable laws. (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3288-6_1

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DOI: 10.1007/978-1-4613-3288-6_1

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