Perturbation analysis for stationary distributions of markov chains with damping component

• Perturbed Markov chains are popular models for description of information networks. In such models, the transition matrix P0 of an information Markov chain is usually approximated by matrix Pε = (1 - ε) P0 + ε D, where D is a so-called damping stochastic matrix with identical rows and all positive elements, while ε is a damping (perturbation) parameter. We perform a detailed perturbation analysis for stationary distributions of such Markov chains, in particular get effective explicit series representations for the corresponding stationary distributions πε, upper bounds for the deviation |πε- π0 |, and asymptotic expansions for πε with respect to the perturbation parameter ε.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Asymptotic expansion

Damping component

Information network

Markov chain

Rate of convergence

Regular perturbation

Singular perturbation

Stationary distribution

Damping

Information services

Matrix algebra

Stochastic models

Stochastic systems

Information networks

Perturbation Analysis

Perturbation parameters

Series representations

Stochastic matrices

Transition matrices

Markov chains

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publication and Content Type

ref (subject category)

kap (subject category)