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Coupling and ergodi...
Coupling and ergodic theorems for Markov chains with damping component
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- Silvestrov, Dmitrii, 1947- (författare)
- Stockholms universitet,Mälardalens universitet,Utbildningsvetenskap och Matematik,MAM,Matematiska institutionen
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- Silvestrov, Sergei, Professor, 1970- (författare)
- Mälardalens universitet,Utbildningsvetenskap och Matematik,MAM
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- Abola, Benard (författare)
- Department of Mathematics, Faculty of Science, Gulu University, Uganda
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- Biganda, Pitos Seleka (författare)
- Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania
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- Engström, Christopher, 1987- (författare)
- Mälardalens universitet,Utbildningsvetenskap och Matematik,MAM
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- Mango, John Magero (författare)
- Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda
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- Kakuba, Gudwin (författare)
- Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda
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Kakuba, Godvingod (författare)
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(creator_code:org_t)
- American Mathematical Society, 2020
- 2020
- Engelska.
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Ingår i: Theory of Probability and Mathematical Statistics. - : American Mathematical Society. - 0094-9000 .- 1547-7363. ; 101, s. 243-264
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- 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
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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