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Malyarenko, AnatoliyORCID iD iconorcid.org/0000-0002-0139-0747
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Publikationer (10 of 106) Visa alla publikationer
Nohrouzian, H., Malyarenko, A. & Ni, Y. (2024). Constructing Trinominal Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives. In: Yiannis Dimotikalis; Christos H. Skiadas (Ed.), Data Analysis and Related Applications 3: Theory and Practice – New Approaches. John Wiley & Sons
Öppna denna publikation i ny flik eller fönster >>Constructing Trinominal Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives
2024 (Engelska)Ingår i: Data Analysis and Related Applications 3: Theory and Practice – New Approaches / [ed] Yiannis Dimotikalis; Christos H. Skiadas, John Wiley & Sons, 2024Kapitel i bok, del av antologi (Refereegranskat)
Ort, förlag, år, upplaga, sidor
John Wiley & Sons, 2024
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:mdh:diva-66530 (URN)9781786309624 (ISBN)
Tillgänglig från: 2024-04-30 Skapad: 2024-04-30 Senast uppdaterad: 2024-04-30Bibliografiskt granskad
Malyarenko, A. & Porcu, E. (2024). Multivariate Random Fields Evolving Temporally Over Hyperbolic Spaces. Journal of theoretical probability
Öppna denna publikation i ny flik eller fönster >>Multivariate Random Fields Evolving Temporally Over Hyperbolic Spaces
2024 (Engelska)Ingår i: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230Artikel i tidskrift (Refereegranskat) Epub ahead of print
Abstract [en]

Gaussian random fields are completely characterised by their mean value and covariance function. Random fields on hyperbolic spaces have been studied to a limited extent only, namely for the case of scalar-valued fields that are not evolving over time. This paper challenges the problem of the second-order characteristics of multivariate (vector-valued) random fields that evolve temporally over hyperbolic spaces. Specifically, we characterise the continuous space–time covariance functions that are isotropic (radially symmetric) over space (the hyperbolic space) and stationary over time (the real line). Our finding is the analogue of recent findings that have been shown for the case where the space is either the n-dimensional sphere or more generally a two-point homogeneous space. Our main result can be read as a spectral representation theorem, and we also detail the main result for the subcase of covariance functions having a spectrum that is absolutely continuous with respect to the Lebesgue measure (technical details are reported below).

Nyckelord
Covariance functions Hyperbolic spaces Multivariate random fields Space–time
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-66157 (URN)10.1007/s10959-024-01316-6 (DOI)001171203300001 ()2-s2.0-85185954270 (Scopus ID)
Forskningsfinansiär
Mälardalens universitet
Tillgänglig från: 2024-02-29 Skapad: 2024-02-29 Senast uppdaterad: 2024-03-20Bibliografiskt granskad
Albuhayri, M., Dimitrov, M., Ni, Y. & Malyarenko, A. (2024). Numerical Studies of Implied Volatility Expansions Under the Gatheral Model. In: Yiannis Dimotikalis; Christos H. Skiadas (Ed.), Data Analysis and Related Applications 3: Theory and Practice – New Approaches. John Wiley & Sons
Öppna denna publikation i ny flik eller fönster >>Numerical Studies of Implied Volatility Expansions Under the Gatheral Model
2024 (Engelska)Ingår i: Data Analysis and Related Applications 3: Theory and Practice – New Approaches / [ed] Yiannis Dimotikalis; Christos H. Skiadas, John Wiley & Sons, 2024Kapitel i bok, del av antologi (Refereegranskat)
Ort, förlag, år, upplaga, sidor
John Wiley & Sons, 2024
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:mdh:diva-66529 (URN)9781786309624 (ISBN)
Tillgänglig från: 2024-04-30 Skapad: 2024-04-30 Senast uppdaterad: 2024-04-30Bibliografiskt granskad
Malyarenko, A. (2024). Probabilistic Models of Cosmic Backgrounds (1ed.). Boca Raton, FL, USA: CRC Press
Öppna denna publikation i ny flik eller fönster >>Probabilistic Models of Cosmic Backgrounds
2024 (Engelska)Bok (Övrigt vetenskapligt)
Abstract [en]

Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fiber bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive description of mathematical and physical aspects of cosmic backgrounds with a clear focus on examples and explicit calculations. Its reader will bridge the gap of misunderstanding between the specialists in various theoretical and applied areas who speak different scientific languages. The audience of the book consists of scholars, students, and professional researchers. A scholar will find basic material for starting their own research. A student will use the book as supplementary material for various courses and modules. A professional mathematician will find a description of several physical phenomena at the rigorous mathematical level. A professional physicist will discover mathematical foundations for well-known physical theories.

Ort, förlag, år, upplaga, sidor
Boca Raton, FL, USA: CRC Press, 2024. s. 259 Upplaga: 1
Serie
Probabilistic Models of Cosmic Backgrounds
Nationell ämneskategori
Matematik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-67195 (URN)10.1201/9781003344353 (DOI)2-s2.0-85194334529 (Scopus ID)9781032381985 (ISBN)9781032382937 (ISBN)9781003344353 (ISBN)
Tillgänglig från: 2024-06-05 Skapad: 2024-06-05 Senast uppdaterad: 2024-08-16
Braiman, V., Malyarenko, A., Mishura, Y. & Rudyk, Y. A. (2024). Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter. Nonlinear Analysis: Modelling and Control, 29(4), 802-815
Öppna denna publikation i ny flik eller fönster >>Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter
2024 (Engelska)Ingår i: Nonlinear Analysis: Modelling and Control, ISSN 1392-5113, E-ISSN 2335-8963, Vol. 29, nr 4, s. 802-815Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We consider two types of entropy, namely, Shannon and R & eacute;nyi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simple, for R & eacute;nyi entropy, which depends on additional parameter alpha > 0, we can characterize it as nontrivial. The proof is based on application of Karamata’s inequality to the terms of Poisson distribution.

Ort, förlag, år, upplaga, sidor
Vilnius University Press, 2024
Nyckelord
Shannon entropy, R & eacute, nyi entropy, Poisson distribution, Karamata’s inequality
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:mdh:diva-68138 (URN)10.15388/namc.2024.29.35560 (DOI)001275011100010 ()2-s2.0-85199638716 (Scopus ID)
Tillgänglig från: 2024-08-07 Skapad: 2024-08-07 Senast uppdaterad: 2024-08-07Bibliografiskt granskad
Malyarenko, A., Mishura, Y., Ralchenko, K. & Shklyar, S. (2023). Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index. Fractional Calculus and Applied Analysis
Öppna denna publikation i ny flik eller fönster >>Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index
2023 (Engelska)Ingår i: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

This paper is devoted to the study of the properties of entropy as a function of the Hurst index, which corresponds to the fractional Gaussian noise. Since the entropy of the Gaussian vector depends on the determinant of the covariance matrix, and the behavior of this determinant as a function of the Hurst index is rather difficult to study analytically at high dimensions, we also consider simple alternative entropy functionals, whose behavior, on the one hand, mimics the behavior of entropy and, on the other hand, is not difficult to study. Asymptotic behavior of the normalized entropy (so called entropy rate) is also studied for the entropy and for the alternative functionals.

Nyckelord
Fractional Gaussian noise, Hurst index, Entropy, Entropy functionals, Entropy rate
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-62415 (URN)10.1007/s13540-023-00155-2 (DOI)000980824200002 ()2-s2.0-85156247682 (Scopus ID)
Forskningsfinansiär
Stiftelsen för strategisk forskning (SSF), UKR22-0017Norges forskningsråd, 274410Norges forskningsråd, 274410
Tillgänglig från: 2023-05-08 Skapad: 2023-05-08 Senast uppdaterad: 2024-01-09Bibliografiskt granskad
Silvestrov, S. & Malyarenko, A. (Eds.). (2023). Non-commutative and Non-associative Algebra and Analysis Structures. Paper presented at SPAS 2019, Västerås, Sweden, September 30 - October 2. Cham: Springer
Öppna denna publikation i ny flik eller fönster >>Non-commutative and Non-associative Algebra and Analysis Structures
2023 (Engelska)Proceedings (redaktörskap) (Refereegranskat)
Abstract [en]

The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019 was to showcase the frontiers of research in several important topics of mathematics, mathematical statistics, and its applications. The conference has been organized along the following tracks: 

1. Stochastic processes and modern statistical methods in theory and practice, 

2. Engineering Mathematics, 

3. Algebraic Structures and applications.  

This book highlights the latest advances in algebraic structures and applications focused on mathematical notions, methods, structures, concepts, problems, algorithms, and computational methods for the natural sciences, engineering, and modern technology. In particular, the book features mathematical methods and models from non-commutative and non-associative algebras and rings associated to generalizations of differential calculus, quantum deformations of algebras, Lie algebras, Lie superalgebras, color Lie algebras, Hom-algebras and their n-ary generalizations, semigroups and group algebras, non-commutative and non-associative algebras and computational algebra interplay with q-special functions and q-analysis, topology, dynamical systems, representation theory, operator theory and functional analysis, applications of algebraic structures in coding theory, information analysis, geometry and probability theory. 

The book gathers selected, high-quality contributed chapters from several large research communities working on modern algebraic structures and their applications. The chapters cover both theory and applications, and are illustrated with a wealth of ideas, theorems, notions, proofs, examples, open problems, and results on the interplay of algebraic structures with other parts of Mathematics. The applications help readers grasp the material, and encourage them to develop new mathematical methods and concepts in their future research. Presenting new methods and results, reviews of cutting-edge research, open problems, and directions for future research, this book will serve as a source of inspiration for a broad range of researchers and students.

Ort, förlag, år, upplaga, sidor
Cham: Springer, 2023
Serie
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 426
Nyckelord
Associate Algebras, Non-associative Algebras, Spectral Analysis, Operator Theory, Deformation Theory, Commutative Algebras, Non-commutative Algebras, Hom-Lie Algebras
Nationell ämneskategori
Algebra och logik Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-68061 (URN)10.1007/978-3-031-32009-5 (DOI)978-3-031-32008-8 (ISBN)978-3-031-32011-8 (ISBN)978-3-031-32009-5 (ISBN)
Konferens
SPAS 2019, Västerås, Sweden, September 30 - October 2
Tillgänglig från: 2024-07-14 Skapad: 2024-07-14 Senast uppdaterad: 2024-07-24Bibliografiskt granskad
Malyarenko, A., Mishura, Y., Ralchenko, K. & Rudyk, Y. A. (2023). Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes. Axioms, 12(11), Article ID 1026.
Öppna denna publikation i ny flik eller fönster >>Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes
2023 (Engelska)Ingår i: Axioms, ISSN 2075-1680, Vol. 12, nr 11, artikel-id 1026Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes.

Ort, förlag, år, upplaga, sidor
Basel: MDPI, 2023
Nyckelord
Shannon entropy; Rényi entropy; Tsallis entropy; Sharma–Mittal entropy; normal distribution; fractional Brownian motion; subfractional Brownian motion; bifractional Brownian motion; multifractional Brownian motion; tempered fractional Brownian motion
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-64641 (URN)10.3390/axioms12111026 (DOI)001120792100001 ()
Forskningsfinansiär
Stiftelsen för strategisk forskning (SSF), UKR22-0017Norges forskningsråd, 274410
Tillgänglig från: 2023-10-31 Skapad: 2023-10-31 Senast uppdaterad: 2024-01-03Bibliografiskt granskad
Malyarenko, A. & Ostoja-Starzewski, M. (2023). Tensor- and spinor-valued random fields with applications to continuum physics and cosmology. Probability Surveys, 20(none), 1-86
Öppna denna publikation i ny flik eller fönster >>Tensor- and spinor-valued random fields with applications to continuum physics and cosmology
2023 (Engelska)Ingår i: Probability Surveys, E-ISSN 1549-5787, Vol. 20, nr none, s. 1-86Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

In this paper, we review the history, current state-of-art, and physical applications of the spectral theory of two classes of random functions. One class consists of homogeneous and isotropic random fields defined on a Euclidean space and taking values in a real finite-dimensional linear space. In applications to continuum physics, such a field describes the physical properties of a homogeneous and isotropic continuous medium in the situation, when a microstructure is attached to all medium points.The range of the field is the fixed point set of a symmetry class, where two compact Lie groups act by orthogonal representations. The material symmetry group of a homogeneous medium is the same at each point and acts trivially, while the group of physical symmetries may act nontrivially. In an isotropic random medium, the rank 1 (resp., rank 2) correlation tensors of the field transform under the action of the group of physical symmetries according to the above representation (resp., its tensor square), making the field isotropic. Another class consists of isotropic random cross-sections of homogeneous vector bundles over a coset space of a compact Lie group. In applications to cosmology, the coset space models the sky sphere, while the random crosssection models a cosmic background. The Cosmological Principle ensures that the cross-section is isotropic.For the convenience of the reader, a necessary material from multilinear algebra, representation theory, and differential geometry is reviewed in Appendix.

Ort, förlag, år, upplaga, sidor
The Hague, The Netherlands: , 2023
Nyckelord
Random field, cosmic microwave background, microstructure, spectral expansion
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-61434 (URN)10.1214/22-ps12 (DOI)000975036600001 ()
Tillgänglig från: 2023-01-05 Skapad: 2023-01-05 Senast uppdaterad: 2023-07-19Bibliografiskt granskad
Muhumuza, A. K., Lundengård, K., Malyarenko, A., Silvestrov, S., Mango, J. M. & Kakuba, G. (2023). The Wishart Distribution on Symmetric Cones. In: Sergei Silvestrov, Anatoliy Malyarenko (Ed.), Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2. Paper presented at International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019 (pp. 661-684). Springer
Öppna denna publikation i ny flik eller fönster >>The Wishart Distribution on Symmetric Cones
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2023 (Engelska)Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, s. 661-684Konferensbidrag, Publicerat paper (Refereegranskat)
Abstract [en]

In this paper we discuss the extension of the Wishart probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions in the field of Herm(m,C), Herm(m,H), Herm(3,O) that denotes respectively the Jordan algebra of all Hermitian matrices of size m× m with complex entries, the skew field H of quaternions, and the algebra O of octonions. This density is characterised by the Vandermonde determinant structure and the exponential weight that is dependent on the trace of the given matrix.

Ort, förlag, år, upplaga, sidor
Springer, 2023
Serie
Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
Nyckelord
Vandermonde determinant, Jordan algebra, Symmetric cone, Wishart distribution
Nationell ämneskategori
Sannolikhetsteori och statistik Algebra och logik Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-64593 (URN)10.1007/978-3-031-32009-5_23 (DOI)2-s2.0-85174443553 (Scopus ID)9783031320088 (ISBN)
Konferens
International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
Tillgänglig från: 2023-10-30 Skapad: 2023-10-30 Senast uppdaterad: 2023-12-27Bibliografiskt granskad
Organisationer
Identifikatorer
ORCID-id: ORCID iD iconorcid.org/0000-0002-0139-0747

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