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Malyarenko, Anatoliyorcid.org/0000-0002-0139-0747

Open this publication in new window or tab >>Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index### Malyarenko, Anatoliy

### Mishura, Yuliiya

### Ralchenko, Kostiantyn

### Shklyar, Sergiy

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}); 2023 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Fractional Gaussian noise, Hurst index, Entropy, Entropy functionals, Entropy rate
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-62415 (URN)10.1007/s13540-023-00155-2 (DOI)000980824200002 ()2-s2.0-85156247682 (Scopus ID)
#####

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##### Funder

Swedish Foundation for Strategic Research, UKR22-0017The Research Council of Norway, 274410The Research Council of Norway, 274410
Available from: 2023-05-08 Created: 2023-05-08 Last updated: 2024-01-09Bibliographically approved

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

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, Ukraine.

Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, Ukraine.

Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, 01601 Kyiv, Ukraine.

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.

Open this publication in new window or tab >>Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes### Malyarenko, Anatoliy

### Mishura, Yuliiya

### Ralchenko, Kostiantyn

### Rudyk, Yevheniia Anastasiia

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}); 2023 (English)In: Axioms, ISSN 2075-1680, Vol. 12, no 11, article id 1026Article in journal (Refereed) Published
##### Abstract [en]

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

Basel: MDPI, 2023
##### Keywords

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
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-64641 (URN)10.3390/axioms12111026 (DOI)001120792100001 ()
#####

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##### Funder

Swedish Foundation for Strategic Research, UKR22-0017The Research Council of Norway, 274410
Available from: 2023-10-31 Created: 2023-10-31 Last updated: 2024-01-03Bibliographically approved

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

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

Sydney Mathematical Research Institute, The University of Sydney, Sydney NSW 2006, Australia.

Taras Shevchenko National Unversity of Kyiv, Ukraine.

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.

Open this publication in new window or tab >>Tensor- and spinor-valued random fields with applications to continuum physics and cosmology### Malyarenko, Anatoliy

### Ostoja-Starzewski, Martin

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}); 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}); 2023 (English)In: Probability Surveys, E-ISSN 1549-5787, Vol. 20, no none, p. 1-86Article in journal (Refereed) Published
##### Abstract [en]

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

The Hague, The Netherlands: , 2023
##### Keywords

Random field, cosmic microwave background, microstructure, spectral expansion
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-61434 (URN)10.1214/22-ps12 (DOI)000975036600001 ()
#####

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Available from: 2023-01-05 Created: 2023-01-05 Last updated: 2023-07-19Bibliographically approved

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

Department of Mechanical Science & Engineering, also Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, 61801-2906 USA .

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.

Open this publication in new window or tab >>The Wishart Distribution on Symmetric Cones### Muhumuza, Asaph Keikara

### Lundengård, Karl

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

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.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}); ### Mango, John Magero

### Kakuba, Godwin

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}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_3_j_idt208_j_idt222",{id:"formSmash:j_idt204:3:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2023 (English)In: Non-commutative and Non-associative Algebra and Analysis Structures: SPAS 2019, Västerås, Sweden, September 30 - October 2 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Springer , 2023, p. 661-684Conference paper, Published paper (Refereed)
##### Abstract [en]

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

Springer, 2023
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 21941009 ; 426
##### Keywords

Vandermonde determinant, Jordan algebra, Symmetric cone, Wishart distribution
##### National Category

Probability Theory and Statistics Algebra and Logic Mathematical Analysis
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-64593 (URN)10.1007/978-3-031-32009-5_23 (DOI)2-s2.0-85174443553 (Scopus ID)9783031320088 (ISBN)
##### Conference

International Conference on Stochastic Processes and Algebraic Structures—From Theory Towards Applications, SPAS 2019, Västerås, Sweden, 30 September - 2 October 2019
#####

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Available from: 2023-10-30 Created: 2023-10-30 Last updated: 2023-12-27Bibliographically approved

Department of Mathematics, Busitema University, Box 236, Tororo, Uganda.

Department of Mathematics, Makerere University, Box 7062, Kampala, Uganda.

Department of Mathematics, Makerere University, Box 7062, Kampala, Uganda.

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.

Open this publication in new window or tab >>A deep look into the Dagum family of isotropic covariance functions### Faouzi, Tarik

### Kondrashuk, Igor

### Porcu, Emilio

### Malyarenko, Anatoliy

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.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}); 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}); 2022 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 59, no 4, p. 1026-1041Article in journal (Refereed) Published
##### Abstract [en]

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

Cambridge: Cambridge University Press, 2022
##### Keywords

Hankel transforms, Mellin–Barnes transforms, spectral theory, positive-definite
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-59770 (URN)10.1017/jpr.2021.103 (DOI)000841660300001 ()2-s2.0-85142135252 (Scopus ID)
#####

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Available from: 2022-08-22 Created: 2022-08-22 Last updated: 2023-04-12Bibliographically approved

Universidad del Bío-Bío, Chile.

Universidad del Bio-Bio, Chile.

Khalifa University at Abu Dhabi, United Arab Emirates..

The Dagum family of isotropic covariance functions has two parameters that allow fordecoupling of the fractal dimension and the Hurst effect for Gaussian random fields thatare stationary and isotropic over Euclidean spaces. Sufficient conditions that allow forpositive definiteness in $R^d$ of the Dagum family have been proposed on the basis ofthe fact that the Dagum family allows for complete monotonicity under some parameter restrictions. The spectral properties of the Dagum family have been inspected to a verylimited extent only, and this paper gives insight into this direction. Specifically, we studyfinite and asymptotic properties of the isotropic spectral density (intended as the Hankeltransform) of the Dagum model. Also, we establish some closed-form expressions forthe Dagum spectral density in terms of the Fox–Wright functions. Finally, we provideasymptotic properties for such a class of spectral densities.

Open this publication in new window or tab >>An Improved Asymptotics of Implied Volatility in the Gatheral Model### Albuhayri, Mohammed

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

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

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

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

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.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..."}); 2022 (English)In: *Springer Proceedings in Mathematics and Statistics*, Springer Nature, 2022, Vol. 408, p. 3-13Conference paper, Published paper (Refereed)
##### Abstract [en]

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

Springer Nature, 2022
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 408
##### Keywords

Double-mean-reverting model, Implied volatility
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-61400 (URN)10.1007/978-3-031-17820-7_1 (DOI)2-s2.0-85171525140 (Scopus ID)978-3-031-17819-1 (ISBN)978-3-031-17820-7 (ISBN)
##### Conference

SPAS 2019, Västerås, Sweden, September 30–October 2
#####

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Available from: 2022-12-31 Created: 2022-12-31 Last updated: 2023-10-04Bibliographically approved

We study the double-mean-reverting model by Gatheral. Our previous results concerning the asymptotic expansion of the implied volatility of a European call option, are improved up to order 3, that is, the error of the approximation is ultimately smaller that the 1.5th power of time to maturity plus the cube of the absolute value of the difference between the logarithmic security price and the logarithmic strike price.

Open this publication in new window or tab >>Connections between the extreme points for Vandermonde determinants and minimizing risk measure in financial mathematics### Muhumuza, Asaph Keikara

### Lundengård, Karl

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

### 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}); ### Mango, John Magero

### Kakuba, Godwin

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}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt204_6_j_idt208_j_idt222",{id:"formSmash:j_idt204:6:j_idt208:j_idt222",widgetVar:"widget_formSmash_j_idt204_6_j_idt208_j_idt222",onLabel:"Hide others...",offLabel:"Show others..."}); 2022 (English)In: *Springer Proceedings in Mathematics and Statistics*, Springer Nature, 2022, p. 587-623Conference paper, Published paper (Refereed)
##### Abstract [en]

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

Springer Nature, 2022
##### Keywords

Asset pricing, Optimal portfolio selection, Risk minimization, Vandermonde determinant
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-61409 (URN)978-3-031-17819-1 (ISBN)
##### Conference

SPAS 2019, Västerås, Sweden, September 30–October 2
#####

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##### Funder

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

Department of Mathematics, Busitema University, Tororo, Uganda.

Mälardalen University, School of Education, Culture and Communication.

Department of Mathematics, Makerere University, Kampala, Uganda.

Department of Mathematics, Makerere University, Kampala, Uganda.

The extreme points of Vandermonde determinants when optimized on surfaces like spheres and cubes have various applications in random matrix theory, electrostatics and financial mathematics. In this study, we apply the extreme points of Vandermonde determinant when optimized on various surfaces to risk minimization in financial mathematics. We illustrate this by constructing the efficient frontiers represented by spheres, cubes and other general surfaces as applies to portfolio theory. The extreme points of Vandermonde determinant lying on such surfaces as efficient frontier would be used to determine the set of assets with minimum risk and maximum returns. This technique can also applied in optimal portfolio selection and asset pricing.

Open this publication in new window or tab >>Constructing Trinomial Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives### Nohrouzian, Hossein

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

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

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}); 2022 (English)Conference paper, Oral presentation with published abstract (Other academic)
##### Abstract [en]

##### Keywords

Cubature method, Stratonovich integral, Wiener space, stochastic market model
##### National Category

Mathematics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-59718 (URN)
##### Conference

7th Stochastic Modeling Techniques and Data Analysis International Conference and Demographics 2022 Workshop
#####

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#####

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Available from: 2022-08-08 Created: 2022-08-08 Last updated: 2022-08-15Bibliographically approved

This contribution deals with an extension to our developed novel cubature methods of degrees 5 on Wiener space. In our previous studies, we studied cubature formulae that are exact for all multiple Stratonovich integrals up to dimension equal to the degree. In fact, cubature method reduces solving a stochastic differential equation to solving a finite set of ordinary differential equations. Now, we apply the above methods to construct trinomial models and to price different financial derivatives. We will compare our numerical solutions with the Black’s and Black-Scholes models’ analytical solutions. The constructed model has practical usage in pricing American options and American-style derivatives.

Open this publication in new window or tab >>EDITORIAL### Malyarenko, Anatoliy

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

### Olenko, A.

### Ostoja-Starzewski, M.

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}); 2022 (English)In: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, ISSN 0094-9000, Vol. 106, p. 1-1Article in journal, Editorial material (Refereed) Published
##### Place, publisher, year, edition, pages

TARAS SHEVCHENKO NATL UNIV KYIV, FAC MECH & MATH, 2022
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-60670 (URN)10.1090/tpms/11722022 (DOI)000804247700001 ()
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_j_idt379",{id:"formSmash:j_idt204:8:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_j_idt379",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_8_j_idt208_j_idt391",{id:"formSmash:j_idt204:8:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_8_j_idt208_j_idt391",multiple:true});
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Available from: 2022-11-21 Created: 2022-11-21 Last updated: 2023-02-08Bibliographically approved

Taras Shevchenko Natl Univ Kyiv, Kiev, Ukraine..

La Trobe Univ, Melbourne, Vic, Australia..

Univ Illinois, Urbana, IL USA..

Open this publication in new window or tab >>EDITORIAL### Malyarenko, Anatoliy

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

### Olenko, A.

### Ostoja-starzewski, M.

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}); 2022 (English)In: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, ISSN 0094-9000, Vol. 106, p. 1-1Article in journal, Editorial material (Other academic) Published
##### Place, publisher, year, edition, pages

TARAS SHEVCHENKO NATL UNIV KYIV, FAC MECH & MATH, 2022
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:mdh:diva-65168 (URN)10.1090/tpms/1172 (DOI)000809405400001 ()2-s2.0-85131427374 (Scopus ID)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_j_idt379",{id:"formSmash:j_idt204:9:j_idt208:j_idt379",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_j_idt379",multiple:true});
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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_9_j_idt208_j_idt391",{id:"formSmash:j_idt204:9:j_idt208:j_idt391",widgetVar:"widget_formSmash_j_idt204_9_j_idt208_j_idt391",multiple:true});
#####

Available from: 2023-12-21 Created: 2023-12-21 Last updated: 2023-12-21Bibliographically approved

Taras Shevchenko Natl Univ Kyiv, Kiev, Ukraine..

La Trobe Univ, Melbourne, Vic, Australia..

Univ Illinois, Urbana, IL USA..