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Markov Skeleton Processes

In: Markov Processes and Controlled Markov Chains

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zhenting Hou & Zaiming Liu & Jiezhong Zou & Xuerong Chen, 2002. "Markov Skeleton Processes," Springer Books, in: Zhenting Hou & Jerzy A. Filar & Anyue Chen (ed.), Markov Processes and Controlled Markov Chains, chapter 0, pages 69-92, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0265-0_5
    DOI: 10.1007/978-1-4613-0265-0_5
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