Convergence of a second order Markov chain

DOI10.1016/j.amc.2014.05.011zbMath1334.60143arXiv1307.6919OpenAlexW2073478238MaRDI QIDQ279270

Liqun Qi, Sheng-Long Hu

Publication date: 27 April 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.6919

zbMATH Keywords

nonnegative tensorsecond-order Markov chaintransition probability tensor

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (17)

Ergodicity Coefficients for Higher-Order Stochastic Processes ⋮ Higher order ergodic Markov chains and first passage times ⋮ Some variational principles for \(Z\)-eigenvalues of nonnegative tensors ⋮ Tristochastic operations and products of quantum states ⋮ Multilinear PageRank: uniqueness, error bound and perturbation analysis ⋮ Second order Markov chains with finite vectors known stationary ⋮ On classification of states in higher order Markov chains ⋮ Ever-reaching probabilities and mean first passage times of higher order ergodic Markov chains ⋮ On the uniqueness of the -eigenvector of transition probability tensors ⋮ Nonnegative tensors revisited: plane stochastic tensors ⋮ Stationary Probability Vectors of Higher-Order Two-Dimensional Symmetric Transition Probability Tensors ⋮ Real eigenvalues of nonsymmetric tensors ⋮ Some bounds for the \(Z\)-eigenpair of nonnegative tensors ⋮ Ergodicity of $p$-majorizing nonlinear Markov operators on the finite dimensional space ⋮ Birkhoff-von Neumann theorem and decomposition for doubly stochastic tensors ⋮ An SDP relaxation method for Perron pairs of a nonnegative tensor ⋮ Solving sparse non-negative tensor equations: algorithms and applications

Cites Work

• Tensor Decompositions and Applications
• Markov chains: models, algorithms and applications
• Perron-Frobenius theorem for nonnegative tensors
• Non-negative matrices and Markov chains. 2nd ed
• Eigenvalues of a real supersymmetric tensor
• Finding the Largest Eigenvalue of a Nonnegative Tensor
• Uniqueness in the Schauder Fixed Point Theorem
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model
• On the limiting probability distribution of a transition probability tensor
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