Markov Skeleton Processes

Zhenting Hou, Zaiming Liu, Jiezhong Zou and Xuerong Chen
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Zhenting Hou: Changsha Railway University, Research Department
Zaiming Liu: Changsha Railway University, Research Department
Jiezhong Zou: Changsha Railway University, Research Department
Xuerong Chen: Changsha Railway University, Research Department

Chapter Chapter 5 in Markov Processes and Controlled Markov Chains, 2002, pp 69-92 from Springer

Abstract: Abstract In this paper, we introduce a new class of stochastic processes - Markov skeleton processes, which have the Markov property at a series of random times. Markov skeleton processes include minimal Q processes, Doob processes, Q processes of order one, Markov processes, semiMarkov processes, piecewise determinate Markov processes, the input processes, the queuing lengths and the waiting times of the system GI/G/1, the insurance risk models, and the option pricing models, as particular cases. The present paper aims to fully expound the background and the history source of the introduction of Markov skeleton processes, and we deduce the forward and backward equation and use them as a powerful tool to obtain the criteria of regularity.

Keywords: Markov skeleton processes; the backward equations; the forward equations; the criteria for the regularity (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0265-0_5

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DOI: 10.1007/978-1-4613-0265-0_5

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