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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zheng-Hai Huang & Liqun Qi, 2020. "Stationary Probability Vectors of Higher-Order Two-Dimensional Symmetric Transition Probability Tensors," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-14, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400199
    DOI: 10.1142/S0217595920400199
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