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On discrete-time stable multiple Markov processes

Author

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  • M. Taghipour
  • A. R. Nematollahi

Abstract

In this paper, we provide necessary conditions for discrete-time symmetric α-stable processes to be linear 2-ple Markov. The aim of this paper is to extend the results given by Adler et al. (1990) to general multiple Markov processes, called linear multiple Markov processes. A necessary and sufficient condition based on the covariation for SαS processes to be linear multiple Markov is provided. A complete description of this class of covariation functions including the stationary case is given. We show that the sum of two independent time-changed Levy motions is linear multiple Markov of order 2. The SαS conditional distributions are also studied, and the conditional characteristic functions of linear 2-ple Markov SαS processes are formed. Finally, we study two famous classes of SαS processes, namely, sub-Gaussian and harmonizable processes, and discuss their Markov properties.

Suggested Citation

  • M. Taghipour & A. R. Nematollahi, 2017. "On discrete-time stable multiple Markov processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1694-1708, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:4:p:1694-1708
    DOI: 10.1080/03610926.2015.1026993
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