On discrete-time stable multiple Markov processes

M. Taghipour and A. R. Nematollahi

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 4, 1694-1708

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.

Date: 2017
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DOI: 10.1080/03610926.2015.1026993

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