The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
From MaRDI portal
Publication:3963813
DOI10.1137/0601031zbMath0498.60071OpenAlexW2127255208MaRDI QIDQ3963813
Publication date: 1980
Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0601031
Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Limit theorems in probability theory (60F99)
Related Items (92)
Unnamed Item ⋮ Stationary distributions of perturbed Markov chains ⋮ A note on formulae for the generalized Drazin inverse of anti-triangular block operator matrices in Banach spaces ⋮ Group inverses of \(M\)-matrices associated with nonnegative matrices having few eigenvalues ⋮ A note on the perturbation bounds of W-weighted Drazin inverse ⋮ Using the QR Factorization and Group Inversion to Compute, Differentiate, and Estimate the Sensitivity of Stationary Probabilities for Markov Chains ⋮ \(M\)-matrix generalized inverses of \(M\)-matrices ⋮ On truncations and perturbations of Markov decision problems with an application to queueing network overflow control ⋮ The computation of key properties of Markov chains via perturbations ⋮ The Drazin inverses of products and differences of orthogonal projections ⋮ On the Smallest Positive Singular Value of a Singular M-Matrix with Applications to Ergodic Markov Chains ⋮ Nonnegative alternating circulants leading to \(M\)-matrix group inverses ⋮ Characterizations of generalized inverses associated with Markovian kernels ⋮ Applications of Paz's inequality to perturbation bounds for Markov chains ⋮ The perturbation bound for the Perron vector of a transition probability tensor ⋮ Acute perturbation of the group inverse ⋮ Explicit formulae for the generalized drazin inverse of block matrices over a Banach algebra ⋮ Representations for the Drazin inverses of \(2 \times 2\) block matrices ⋮ Transition matrices for well-conditioned Markov chains ⋮ Perturbation analysis for dynamic poverty indexes ⋮ Asymptotic behaviour of the survival probabilities in an inhomogeneous semi-Markov model for the migration process in credit risk ⋮ Perturbation bound for the Drazin inverse of the matrix-value function ⋮ Perturbation and Inverse Problems of Stochastic Matrices ⋮ Kemeny's constant for countable Markov chains ⋮ Exact expressions for the Drazin inverse of anti-triangular matrices ⋮ A note on the perturbation bound of the Drazin inverse ⋮ Generalized inverses and a block-rank equation. ⋮ On the Drazin inverse of anti-triangular block matrices ⋮ Perturbation bounds for the group inverse and its oblique projection ⋮ LU decomposition of M-matrices by elimination without pivoting ⋮ Perturbation bounds for Markov chains with general state space ⋮ Group generalized inverses of M-matrices associated with periodic and nonperiodic jacobi matrices ⋮ Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes ⋮ Unnamed Item ⋮ LU decompositions of generalized diagonally dominant matrices ⋮ Unnamed Item ⋮ Generalized inverses of Markovian kernels in terms of properties of the Markov chain ⋮ Improved bounds for a condition number for Markov chains ⋮ Acute perturbation of Drazin inverse and oblique projectors ⋮ Unnamed Item ⋮ Error bounds for state space truncation of finite Jackson networks ⋮ Drazin Invertibility in a Certain Finite-Dimensional Algebra Generated by Two Idempotents ⋮ Some additive results on Drazin inverse ⋮ On Perturbation Bounds for the Joint Stationary Distribution of Multivariate Markov Chain Models ⋮ A Google-like model of road network dynamics and its application to regulation and control ⋮ On optimal condition numbers for Markov chains ⋮ Representations for the Drazin inverse of the sum \(P+Q+R+S\) and its applications ⋮ Strong stability and perturbation bounds for discrete Markov chains ⋮ Reverse order laws for the Drazin inverses ⋮ On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces ⋮ The Role of Kemeny's Constant in Properties of Markov Chains ⋮ On the Variances and Convariances of the Duration State Sizes of Semi-Markov Systems ⋮ Reverse order law for the group inverses ⋮ New perturbation bounds for denumerable Markov chains ⋮ From differential to difference importance measures for Markov reliability models ⋮ Additive perturbation results for the Drazin inverse ⋮ Comparison of perturbation bounds for the stationary distribution of a Markov chain ⋮ Mixing times with applications to perturbed Markov chains ⋮ An improvement on the perturbation of the group inverse and oblique projection ⋮ A note on computational formulas for the Drazin inverse of certain block matrices ⋮ The Drazin inverses of sum and difference of idempotents ⋮ The Drazin inverse of the sum of four matrices and its applications ⋮ A note on the perturbation of an outer inverse ⋮ Bounds on the subdominant eigenvalue involving group inverse with applications to graphs ⋮ A Structured Condition Number for Kemeny's Constant ⋮ Unnamed Item ⋮ Explicit representations of the Drazin inverse of block matrix and modified matrix ⋮ Stationary distribution and perturbation bounds for a stochastic inventory model ⋮ The Drazin inverse of updating of a square matrix with application to perturbation formula ⋮ A note on additive results for the Drazin inverse ⋮ An expression of the Drazin inverse of a perturbed matrix ⋮ Digraph-based conditioning for Markov chains ⋮ Perturbation theory for Moore-Penrose inverse of tensor via Einstein product ⋮ Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero ⋮ Error bounds for the perturbation of the Drazin inverse under some geometrical conditions ⋮ Error bounds for nonnegative dynamic models ⋮ Impact of Varying Community Networks on Disease Invasion ⋮ On the perturbation of the group inverse and oblique projection ⋮ The Drazin inverse of anti-triangular block matrices ⋮ The perturbed nonhomogeneous Markov system ⋮ A note on the perturbation bounds of W-weighted Drazin inverse of linear operator in Banach space ⋮ Markov chain sensitivity measured by mean first passage times ⋮ Regular Markov chains for which the transition matrix has large exponent ⋮ Stationary distributions and mean first passage times of perturbed Markov chains ⋮ Perturbation bound of the Drazin inverse ⋮ The Drazin inverse of a modified matrix ⋮ Error bounds for a general perturbation of the Drazin inverse ⋮ Sharp Entrywise Perturbation Bounds for Markov Chains ⋮ Analytical perturbations in Markov chains ⋮ Some results on the Drazin inverse of anti-triangular matrices ⋮ Sensitivity of the stationary distribution vector for an ergodic Markov chain ⋮ Additive results for the generalized Drazin inverse
Cites Work
- Continuity properties of the Drazin pseudoinverse
- Some applications of a minimum principle in linear algebra
- The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
- The Index and the Drazin Inverse of Block Triangular Matrices
- Perturbation theory and finite Markov chains
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities