References
- Bozorgmanesh H, Hajarian M. Convergence of a transition probability tensor of a higher-order Markov chain to the stationary probability vector. Numer Linear Algebra Appl. 2016;23:972–988.
- Chang KC, Qi L, Zhang T. A survey of the spectral theory of nonnegative tensors. Numer Linear Algebra Appl. 2013;20:891–912.
- Chang KC, Zhang T. On the uniqueness and non-uniqueness of the positive Z-eigenvector for transition probability tensors. J Math Anal Appl. 2013;408:525–540.
- Cui L, Song Y. On the uniqueness of the positive Z-eigenvector for nonnegative tensors. J Comput Appl Math. 2019;352:72–78.
- Culp J, Pearson K, Zhang T. On the uniqueness of the Z1-eigenvector of transition probability tensors. Linear Multilinear Algebra. 2017;65(5):891–896.
- Han L, Wang K, Xu J. Higher order ergodic Markov chains and first passage times. Linear Multilinear Algebra. 2021;1–8, in press. doi:10.1080/03081087.2021.1968782
- Hu S, Qi L. Convergence of a second order Markov chain. Appl Math Comput. 2014;241:183–192.
- Huang ZH, Qi L. Stationary probability vectors of higher-order two-dimensional symmetric transition probability tensors. Asia Pac J Oper Res. 2020;37(4):2040019.
- Li CK, Zhang S. Stationary probability vectors of higher-order Markov chains. Linear Algebra Appl. 2016;473:114–125.
- Li W, Ng M. On the limiting probability distribution of a transition probability tensor. Linear Multilinear Algebra. 2014;62(3):362–385.
- Qi L, Luo Z. Tensor analysis: spectral theory and special tensors. Philadelphia (PA): SIAM; 2017.
- Raftery A. A model of high-order Markov chains. J R Stat Soc Ser B. 1985;47:528–539.
- Raftrey A, Tavare S. Estimation and modelling repeated patterns in high order Markov chains with the mixture transition distribution model. Appl Stat. 1994;43:179–199.
- Berman A, Plemmons RJ Nonnegative matrices in the mathematical sciences. Classics in applied mathematics. Philadelphia (PA): SIAM; 1994.
- Kemeny JG, Snell JL. Finite Markov chains. Princeton (NJ): Van Nostrand; 1960.
- Hunter JJ. Mathematical techniques of applied probability. Discrete time models: basic theory; vol. 1. New York: Academic Press; 1983.
- Hunter JJ. Mathematical techniques of applied probability. Discrete time models: techniques and applications; vol. 2. New York: Academic Press; 1983.
- Kirkland S, Neumann M. Group inverses of M-matrices and their applications. Boca Raton (FL): CRC Press; 2012.