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Silvestrov, Dmitriiorcid.org/0000-0002-2626-5598

Open this publication in new window or tab >>Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes### Silvestrov, Dmitrii

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_some",{id:"formSmash:j_idt204:0:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_otherAuthors",{id:"formSmash:j_idt204:0:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_otherAuthors",multiple:true}); 2022 (English)Book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer Cham, 2022. p. xvii+401 Edition: 1
##### Keywords

Semi-Markov type process, Rare event, Hitting time, Limit theorem
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-60273 (URN)10.1007/978-3-030-92403-4 (DOI)2-s2.0-85152326433 (Scopus ID)978-3-030-92402-7 (ISBN)978-3-030-92403-4 (ISBN)
#####

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Available from: 2022-10-18 Created: 2022-10-18 Last updated: 2023-09-12Bibliographically approved

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.

This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes; new asymptotic recurrent algorithms of phase space reduction and effective conditions of weak convergence for distributions of hitting times and convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes.

Open this publication in new window or tab >>Perturbed Semi-Markov Type Processes II: Ergodic Theorems for Multi-Alternating Regenerative Processes### Silvestrov, Dmitrii

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2022 (English)Book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer Cham, 2022. p. xvii+413 Edition: 1
##### Keywords

Semi-Markov type process, Ergodic theorem
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-60274 (URN)10.1007/978-3-030-92399-0 (DOI)2-s2.0-85142916498 (Scopus ID)978-3-030-92398-3 (ISBN)978-3-030-92399-0 (ISBN)
#####

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Available from: 2022-10-18 Created: 2022-10-18 Last updated: 2024-01-23Bibliographically approved

Mälardalen University, School of Education, Culture and Communication.

This book is the second volume of two volumes monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and alternating regenerative processes with semi-Markov modulation. The second volume presents new super-long, long and short time ergodic theorems for perturbed alternating regenerative processes and multi-alternating regenerative processes modulating by regularly and singularly perturbed finite semi-Markov processes.

Open this publication in new window or tab >>Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks### Abola, Benard

### Biganda, Pitos

### Silvestrov, Sergei

### Silvestrov, Dmitrii

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); ### Engström, Christopher

### Mango, John Magero

### Kakuba, Godwin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_2_j_idt208_j_idt222",{id:"formSmash:j_idt204:2:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2021 (English)In: Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas, Hoboken, NJ: John Wiley & Sons, 2021, p. 23-55Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Hoboken, NJ: John Wiley & Sons, 2021
##### Series

Big Data, Artificial Intelligence and Data Analysis Set coordinated by Jacques Janssen ; 7
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-56067 (URN)10.1002/9781119821588.ch2 (DOI)2-s2.0-85148063514 (Scopus ID)978-1-786-30673-9 (ISBN)978-1-119-82156-4 (ISBN)
#####

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##### Funder

Sida - Swedish International Development Cooperation Agency
Available from: 2021-10-01 Created: 2021-10-01 Last updated: 2023-04-13Bibliographically approved

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.

Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

This chapter is devoted to studies of perturbed Markov chains, commonly used for the description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularized by adding aspecial damping matrix, multiplied by a small damping (perturbation) parameter ε. In this chapter, we present the results of detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis.

Open this publication in new window or tab >>Convergence in distribution for randomly stopped random fields### Silvestrov, Dmitrii

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 105, p. 137-149Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Kyiv: American Mathematical Society (AMS), 2021
##### Keywords

Random field, random stopping, convergence in distribution
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-60275 (URN)10.1090/tpms/1160 (DOI)000729866100009 ()2-s2.0-85130251621 (Scopus ID)
#####

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Available from: 2022-10-18 Created: 2022-10-18 Last updated: 2022-10-18Bibliographically approved

Let X and Y be two complete, separable, metric spaces, xi(epsilon)(x), x is an element of X and nu(epsilon) be, for every epsilon is an element of[0, 1], respectively, a random field taking values in space Y and a random variable taking values in space X. We present general conditions for convergence in distribution for random variables xi(epsilon)(nu(epsilon)) that is the conditions insuring holding of relation, xi(epsilon)(nu(epsilon)) d ->xi(0)(nu(0)) as epsilon -> 0.

Open this publication in new window or tab >>Coupling and ergodic theorems for markov chains with damping component### Silvestrov, Dmitrii

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Abola, Benard

### Biganda, P. S.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); ### Engström, Christopher

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Mango, J. M.

### Kakuba, G.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_4_j_idt208_j_idt222",{id:"formSmash:j_idt204:4:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2020 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 101, p. 243-264Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Mathematical Society, 2020
##### Keywords

Coupling, Damping component, Ergodic theorem, Information network, Markov chain, Rate of convergence, Regular perturba-tion, Singular perturbation, Triangular array mode
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-62503 (URN)10.1090/tpms/1124 (DOI)2-s2.0-85099421096 (Scopus ID)
#####

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##### Note

Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Dar es Salaam, Tanzania.

Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

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.

Article; Export Date: 11 May 2023; Cited By: 0

Available from: 2023-06-08 Created: 2023-06-08 Last updated: 2023-06-08Bibliographically approvedOpen this publication in new window or tab >>Perturbation analysis for stationary distributions of markov chains with damping component### Silvestrov, Dmitrii

### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Abola, Benard

### Biganda, Pitos

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); ### Engström, Christopher

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Mango, John Magero

### Kakuba, Godwin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_5_j_idt208_j_idt222",{id:"formSmash:j_idt204:5:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2020 (English)In: Algebraic Structures and Applications / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic, Springer Nature, 2020, Vol. 317, p. 903-933Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer Nature, 2020
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 317
##### Keywords

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
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-49438 (URN)10.1007/978-3-030-41850-2_38 (DOI)2-s2.0-85087534079 (Scopus ID)9783030418496 (ISBN)
##### Conference

International Conference on Stochastic Processes and Algebraic Structures, SPAS 2017, 4 October 2017 through 6 October 2017
#####

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##### Funder

Sida - Swedish International Development Cooperation Agency
Available from: 2020-07-15 Created: 2020-07-15 Last updated: 2020-10-22Bibliographically approved

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.

Makerere University, Kampala, Uganda.

Makerere University, Kampala, Uganda.

Perturbed Markov chains are popular models for description of information networks. In such models, the transition matrix P_{0} of an information Markov chain is usually approximated by matrix P_{ε} = (1 - ε) P_{0} + 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 π_{ε}, upper bounds for the deviation |π_{ε}- π_{0} |, and asymptotic expansions for πε with respect to the perturbation parameter ε.

Open this publication in new window or tab >>Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. II### Silvestrov, Dmitrii

### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_some",{id:"formSmash:j_idt204:6:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_6_j_idt208_otherAuthors",{id:"formSmash:j_idt204:6:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_otherAuthors",multiple:true}); 2016 (English)Report (Other academic)
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-33087 (URN)
#####

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Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2017-10-03Bibliographically approved

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.

Open this publication in new window or tab >>Asymptotic expansions for stationary distributions of perturbed semi-Markov processes### Silvestrov, Dmitrii

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_some",{id:"formSmash:j_idt204:7:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_7_j_idt208_otherAuthors",{id:"formSmash:j_idt204:7:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_7_j_idt208_otherAuthors",multiple:true}); 2016 (English)Report (Other academic)
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-33086 (URN)
#####

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Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2017-10-03Bibliographically approved

Open this publication in new window or tab >>Stochastic Approximation Methods for American Type Options### Silvestrov, Dmitrii

### Li, Y.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_some",{id:"formSmash:j_idt204:8:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_otherAuthors",{id:"formSmash:j_idt204:8:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_otherAuthors",multiple:true}); 2016 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 6, p. 1607-1631Article in journal (Refereed) Published
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-23092 (URN)10.1080/03610926.2014.915046 (DOI)000372556000003 ()2-s2.0-84960540164 (Scopus ID)
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Available from: 2013-12-02 Created: 2013-12-02 Last updated: 2017-12-06Bibliographically approved

Stockholm Univ., Sweden.

Stockholm Univ., Sweden.

Open this publication in new window or tab >>American-Type Options, Stochastic Approximation Methods, Volume 2### Silvestrov, Dmitrii

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Stockholm University, Sweden.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_some",{id:"formSmash:j_idt204:9:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_otherAuthors",{id:"formSmash:j_idt204:9:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_otherAuthors",multiple:true}); 2015 (English)Book (Refereed)
##### Place, publisher, year, edition, pages

De Gruyter, 2015. p. 559
##### Series

De Gruyter Studies in Mathematics ; 57
##### Keywords

American option, Optimal stopping, Convergence of rewards, Markov chain, Approximation algorithm
##### National Category

Mathematics Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-27269 (URN)10.1515/9783110329841 (DOI)978-3-11-032984-1 (ISBN)
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Available from: 2015-01-02 Created: 2015-01-02 Last updated: 2017-10-03Bibliographically approved