Stationary Probability Vectors of Higher-Order Two-Dimensional Symmetric Transition Probability Tensors

Zheng-Hai Huang and Liqun Qi ()
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Zheng-Hai Huang: School of Mathematics, Tianjin University, No. 135, Yaguan Road, Tianjin 300350, P. R. China
Liqun Qi: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-14

Abstract: In this paper, we investigate stationary probability vectors of higher-order two-dimensional symmetric transition probability tensors. We show that there are two special symmetric transition probability tensors of order m dimension 2, which have and only have two stationary probability vectors; and any other symmetric transition probability tensor of order m dimension 2 has a unique stationary probability vector. As a byproduct, we obtain that any symmetric transition probability tensor of order m dimension 2 has a unique positive stationary probability vector, and that any symmetric irreducible transition probability tensor of order m dimension 2 has a unique stationary probability vector.

Keywords: Transition probability tensor; higher-order Markov chain; stationary probability vector; eigenvalue of tensor (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400199

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