scholarly journals Applications of Paz's inequality to perturbation bounds for Markov chains

1998 ◽  
Vol 268 ◽  
pp. 183-196 ◽  
Author(s):  
Stephen J. Kirkland ◽  
Michael Neumann ◽  
Bryan L. Shader
Keyword(s):  
Markov Chains ◽  
Perturbation Bounds

scholarly journals Sharp Entrywise Perturbation Bounds for Markov Chains

2015 ◽  
Vol 36 (3) ◽  
pp. 917-941 ◽  
Author(s):  
Erik Thiede ◽  
Brian Van Koten ◽  
Jonathan Weare
Keyword(s):  
Markov Chains ◽  
Perturbation Bounds

scholarly journals Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 253 ◽  
Author(s):  
Alexander Zeifman ◽  
Victor Korolev ◽  
Yacov Satin
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Continuous Time ◽  
Countable State Space ◽  
Perturbation Bounds ◽  
Queuing Models ◽  
Continuous Time Markov Chains ◽  
Quantitative Estimates ◽  
Countable State

This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the construction of perturbation estimates for the main five classes of such chains associated with queuing models. Several specific models are considered for which the limit characteristics and perturbation bounds for admissible “perturbed” processes are calculated.

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (04) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

The spectral gap and perturbation bounds for reversible continuous-time Markov chains

2004 ◽  
Vol 41 (4) ◽  
pp. 1219-1222 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Spectral Gap ◽  
Complete Information ◽  
Stationary States ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
Distribution Vector

We show that, for reversible continuous-time Markov chains, the closeness of the nonzero eigenvalues of the generator to zero provides complete information about the sensitivity of the distribution vector to perturbations of the generator. Our results hold for both the transient and the stationary states.

scholarly journals Sensitivity and convergence of uniformly ergodic Markov chains

2005 ◽  
Vol 42 (4) ◽  
pp. 1003-1014 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Rate Of Convergence ◽  
Transition Kernel ◽  
Numerical Examples ◽  
Perturbation Bounds ◽  
Finite State ◽  
New Perturbation ◽  
Finite State Space

For uniformly ergodic Markov chains, we obtain new perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity. In particular, we derive sensitivity bounds in terms of the ergodicity coefficient of the iterated transition kernel, which improve upon the bounds obtained by other authors. We discuss convergence bounds that hold in the case of finite state space, and consider numerical examples to compare the accuracy of different perturbation bounds.

scholarly journals Sensitivity and convergence of uniformly ergodic Markov chains

2005 ◽  
Vol 42 (04) ◽  
pp. 1003-1014 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Rate Of Convergence ◽  
Transition Kernel ◽  
Numerical Examples ◽  
Perturbation Bounds ◽  
Finite State ◽  
New Perturbation ◽  
Finite State Space

For uniformly ergodic Markov chains, we obtain new perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity. In particular, we derive sensitivity bounds in terms of the ergodicity coefficient of the iterated transition kernel, which improve upon the bounds obtained by other authors. We discuss convergence bounds that hold in the case of finite state space, and consider numerical examples to compare the accuracy of different perturbation bounds.

Uniform ergodicities and perturbation bounds of Markov chains on base norm spaces

2018 ◽  
Vol 41 (6) ◽  
pp. 863-876 ◽  
Author(s):  
Nazife Erkurşun-Özcan ◽  
Farrukh Mukhamedov
Keyword(s):  
Markov Chains ◽  
Perturbation Bounds ◽  
Base Norm

scholarly journals New perturbation bounds for denumerable Markov chains

2010 ◽  
Vol 432 (7) ◽  
pp. 1627-1649 ◽  
Author(s):  
Zahir Mouhoubi ◽  
Djamil Aïssani
Keyword(s):  
Markov Chains ◽  
Perturbation Bounds ◽  
New Perturbation
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