Stationary probability vectors of higher-order two-dimensional transition probability tensors

Zheng-Hai Huang; Liqun Qi

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arXiv · 1802.10270

Stationary probability vectors of higher-order two-dimensional transition probability tensors

Zheng-Hai Huang·Liqun Qi

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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.

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BibTeX RIS

Zheng-Hai Huang, Liqun Qi. 2018-02-28. Stationary probability vectors of higher-order two-dimensional transition probability tensors. https://arxiv.org/abs/1802.10270

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