Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 78, Issue 3, Pages 1008-1025Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2019.03.016
Keywords
Eigenpair; Tensor; Higher-order; Multivariate; Markov chain; Stationary probability distribution
Categories
Funding
- National Natural Science Foundation of China [11671158, 11771159, U181164]
- Major Project of Guangdong Provincial Universities [2016KZDXM025]
- Innovation Team Project of Guangdong Provincial Universities [2015KCXTD007]
- HKRGC GRF [12302715, 12306616, 12200317, 12300218, 15210815]
- IMR, Faculty of Science, The University of Hong Kong
- RAE, Faculty of Science, The University of Hong Kong
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In this paper, we study a new tensor eigenvalue problem, which involves E- and S-eigenvalues as its special cases. Some theoretical results such as existence of an eigenvalue and the number of eigenvalues are given. For an application of the proposed eigenvalue problem, we establish a tensor model for a higher-order multivariate Markov chain. The core issue of this problem is to study a stationary probability distribution of a higher-order multivariate Markov chain. A sufficient condition of the unique stationary positive distribution is given. An algorithm for computing stationary probability distribution is also developed. Numerical examples of applications in stock market modeling, sales demand prediction and biological sequence analysis are given to illustrate the proposed tensor model and the computed stationary probability distribution can provide a better prediction in these Markov chain applications. (C) 2019 Elsevier Ltd. All rights reserved.
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