Probabilistic approach to Perron root, the group inverse, and applications

DOI10.1080/03081087.2011.559167zbMath1239.15008OpenAlexW2080268651MaRDI QIDQ2879637

Michael Neumann, Iddo Ben-Ari

Publication date: 29 March 2012

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

Full work available at URL: https://doi.org/10.1080/03081087.2011.559167

zbMATH Keywords

Markov chainsnonnegative matricescentral limit theoremadditive functionalPerron-Frobenius theorygroup inversesirreducible matricesPerron roots

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Theory of matrix inversion and generalized inverses (15A09) Numerical analysis or methods applied to Markov chains (65C40) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Martingales with continuous parameter (60G44)

Related Items (6)

The computation of key properties of Markov chains via perturbations ⋮ Inequalities for functions of transition matrices ⋮ Generalized inverses of Markovian kernels in terms of properties of the Markov chain ⋮ Asymptotic and non-asymptotic analysis for a hidden Markovian process with a quantum hidden system ⋮ A Probabilistic Approach to Generalized Zeckendorf Decompositions ⋮ Information geometry approach to parameter estimation in hidden Markov model

Cites Work

• Markov additive processes. I: Eigenvalue properties and limit theorems
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• Mixing times with applications to perturbed Markov chains
• On a Question Concerning Condition Numbers for Markov Chains
• Random evolutions and the spectral radius of a non-negative matrix
• A CONVEXITY PROPERTY OF POSITIVE MATRICES
• Markov Chains and Stochastic Stability
• Convex spectral functions
• Probability with Martingales
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Kemeny's Constant and the Random Surfer
• On the Elasticity of the Perron Root of a Nonnegative Matrix

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