On the uniqueness of the -eigenvector of transition probability tensors

DOI10.1080/03081087.2016.1211130zbMath1360.15012OpenAlexW2476057826MaRDI QIDQ2979469

Tan Zhang, Jordan Culp, Kelly Jeanne Pearson

Publication date: 25 April 2017

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2016.1211130

zbMATH Keywords

transition probability tensoreigenvalues for tensors

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69)

Related Items (9)

Higher order ergodic Markov chains and first passage times ⋮ On classification of states in higher order Markov chains ⋮ Ever-reaching probabilities and mean first passage times of higher order ergodic Markov chains ⋮ Improved uniqueness conditions of solution for multilinear pagerank and its application ⋮ Stationary Probability Vectors of Higher-Order Two-Dimensional Symmetric Transition Probability Tensors ⋮ Upper bounds for eigenvalues of Cauchy-Hankel tensors ⋮ Upper bounds for Z\(_1\)-eigenvalues of generalized Hilbert tensors ⋮ New uniqueness conditions for the stationary probability matrix of transition probability tensors ⋮ Birkhoff-von Neumann theorem and decomposition for doubly stochastic tensors

Uses Software

• CoCoA
• Mathematica

Cites Work

• Convergence of a second order Markov chain
• Some variational principles for \(Z\)-eigenvalues of nonnegative tensors
• Perron-Frobenius theorem for nonnegative tensors
• On the uniqueness and non-uniqueness of the positive \(\mathcal Z\)-eigenvector for transition probability tensors
• Eigenvalues of a real supersymmetric tensor
• On the limiting probability distribution of a transition probability tensor

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