Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2

Silvestrov, Dmitrii; Silvestrov, Sergei

doi:10.1007/s11009-017-9607-y

Cited by 4 publications

(1 citation statement)

References 3 publications

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“…We refer here to some recent books and papers devoted to perturbation problems for Markov type processes, [4,5,10,12,20,24,29,30,31,34,35,36,37,46,47,49,50,51,52,53,54,55,58,59]. In particular, we would like to mention works [4,24,49,50], where the extended bibliographies of works in the area and the corresponding methodological and historical remarks can be found.…”

Section: Introductionmentioning

confidence: 99%

Perturbed Markov Chains and Information Networks

Abola,

Biganda,

Silvestrov

et al. 2019

Preprint

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The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, as well as explicit upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities in triangular array mode, where perturbation parameter ε → 0 and n → ∞, simultaneously. The results of numerical experiments are also presented.

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Section: Introductionmentioning

confidence: 99%

Perturbed Markov Chains and Information Networks

Abola,

Biganda,

Silvestrov

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Perturbation Analysis for Stationary Distributions of Markov Chains with Damping Component

Silvestrov

Abola

et al. 2020

Springer Proceedings in Mathematics &Amp; Statistics

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Perturbed Markov Chains with Damping Component

Silvestrov

Abola

et al. 2020

Methodol Comput Appl Probab

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The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.

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Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. 2

Cited by 4 publications

References 3 publications

Perturbed Markov Chains and Information Networks

Perturbed Markov Chains and Information Networks

Perturbation Analysis for Stationary Distributions of Markov Chains with Damping Component

Perturbed Markov Chains with Damping Component

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