Abstract
SUMMARYIn this paper, we study the perturbation bound for the Perron vector of an mth‐order n‐dimensional transition probability tensor with and . The Perron vector x associated to the largest Z‐eigenvalue 1 of , satisfies where the entries xi of x are non‐negative and . The main contribution of this paper is to show that when is perturbed to an another transition probability tensor by , the 1‐norm error between x and is bounded by m, , and the computable quantity related to the uniqueness condition for the Perron vector of . Based on our analysis, we can derive a new perturbation bound for the Perron vector of a transition probability matrix which refers to the case of m = 2. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis. Copyright © 2013 John Wiley & Sons, Ltd.
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