Coupling and ergodic theorems for 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 + εD, where D is a so-called damping stochastic matrix with identical rows and all positive elements, while ε ∈ [0, 1] is a damping (perturbation) parameter. Using procedure of artificial regeneration for the perturbed Markov chain ηε,n, with the matrix of transition probabilities Pε, and coupling methods, we get ergodic theorems, in the form of asymptotic relations for pε,ij (n) = Pi {ηε,n = j} as n → ∞ and ε → 0, and explicit upper bounds for the rates of convergence in such theorems. In particular, the most difficult case of the model with singular perturbations, where the phase space of the unperturbed Markov chain η0,n split in several closed classes of communicative states and possibly a class of transient states, is investigated.

Ämnesord

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

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

Nyckelord

Coupling

Damping component

Ergodic theorem

Information network

Markov chain

Rate of convergence

Regular perturba-tion

Singular perturbation

Triangular array mode

Mathematics/Applied Mathematics

matematik/tillämpad matematik

matematik

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