https://www.mdu.se/

mdu.sePublications
Change search
Link to record
Permanent link

Direct link
Alternative names
Publications (10 of 84) Show all publications
Silvestrov, D. (2022). Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes (1ed.). Springer Cham
Open this publication in new window or tab >>Perturbed Semi-Markov Type Processes I: Limit Theorems for Rare-Event Times and Processes
2022 (English)Book (Refereed)
Abstract [en]

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.

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)
Available from: 2022-10-18 Created: 2022-10-18 Last updated: 2023-09-12Bibliographically approved
Silvestrov, D. (2022). Perturbed Semi-Markov Type Processes II: Ergodic Theorems for Multi-Alternating Regenerative Processes (1ed.). Springer Cham
Open this publication in new window or tab >>Perturbed Semi-Markov Type Processes II: Ergodic Theorems for Multi-Alternating Regenerative Processes
2022 (English)Book (Refereed)
Abstract [en]

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. 

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)
Available from: 2022-10-18 Created: 2022-10-18 Last updated: 2024-01-23Bibliographically approved
Abola, B., Biganda, P., Silvestrov, S., Silvestrov, D., Engström, C., Mango, J. M. & Kakuba, G. (2021). Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks. In: Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas (Ed.), Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools (pp. 23-55). Hoboken, NJ: John Wiley & Sons
Open this publication in new window or tab >>Chapter 2. Nonlinearly Perturbed Markov Chains and Information Networks
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]

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.

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)
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2021-10-01 Created: 2021-10-01 Last updated: 2023-04-13Bibliographically approved
Silvestrov, D. (2021). Convergence in distribution for randomly stopped random fields. Theory of Probability and Mathematical Statistics, 105, 137-149
Open this publication in new window or tab >>Convergence in distribution for randomly stopped random fields
2021 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 105, p. 137-149Article in journal (Refereed) Published
Abstract [en]

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.

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)
Available from: 2022-10-18 Created: 2022-10-18 Last updated: 2022-10-18Bibliographically approved
Silvestrov, D., Silvestrov, S., Abola, B., Biganda, P. S., Engström, C., Mango, J. M. & Kakuba, G. (2020). Coupling and ergodic theorems for markov chains with damping component. Theory of Probability and Mathematical Statistics, 101, 243-264
Open this publication in new window or tab >>Coupling and ergodic theorems for markov chains with damping component
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]

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.

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)
Note

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

Available from: 2023-06-08 Created: 2023-06-08 Last updated: 2023-06-08Bibliographically approved
Silvestrov, D., Silvestrov, S., Abola, B., Biganda, P., Engström, C., Mango, J. M. & Kakuba, G. (2020). Perturbation analysis for stationary distributions of markov chains with damping component. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic (Ed.), Algebraic Structures and Applications: . Paper presented at International Conference on Stochastic Processes and Algebraic Structures, SPAS 2017, 4 October 2017 through 6 October 2017 (pp. 903-933). Paper presented at International Conference on Stochastic Processes and Algebraic Structures, SPAS 2017, 4 October 2017 through 6 October 2017. Springer Nature, 317
Open this publication in new window or tab >>Perturbation analysis for stationary distributions of markov chains with damping component
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]

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.

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
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2020-07-15 Created: 2020-07-15 Last updated: 2020-10-22Bibliographically approved
Silvestrov, D. & Silvestrov, S. (2016). Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. II.
Open this publication in new window or tab >>Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. II
2016 (English)Report (Other academic)
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33087 (URN)
Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2017-10-03Bibliographically approved
Silvestrov, D. & Silvestrov, S. (2016). Asymptotic expansions for stationary distributions of perturbed semi-Markov processes.
Open this publication in new window or tab >>Asymptotic expansions for stationary distributions of perturbed semi-Markov processes
2016 (English)Report (Other academic)
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-33086 (URN)
Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2017-10-03Bibliographically approved
Silvestrov, D. & Li, Y. (2016). Stochastic Approximation Methods for American Type Options. Communications in Statistics - Theory and Methods, 45(6), 1607-1631
Open this publication in new window or tab >>Stochastic Approximation Methods for American Type Options
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)
Available from: 2013-12-02 Created: 2013-12-02 Last updated: 2017-12-06Bibliographically approved
Silvestrov, D. (2015). American-Type Options, Stochastic Approximation Methods, Volume 2. De Gruyter
Open this publication in new window or tab >>American-Type Options, Stochastic Approximation Methods, Volume 2
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)
Available from: 2015-01-02 Created: 2015-01-02 Last updated: 2017-10-03Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2626-5598

Search in DiVA

Show all publications