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Malyarenko, AnatoliyORCID iD iconorcid.org/0000-0002-0139-0747
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Publications (10 of 58) Show all publications
Karimi, P., Malyarenko, A., Ostoja-Starzewski, M. & Zhang, X. (2020). RVE problem: mathematical aspects and related stochastic mechanics. International Journal of Engineering Science, 146, Article ID 103169.
Open this publication in new window or tab >>RVE problem: mathematical aspects and related stochastic mechanics
2020 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 146, article id 103169Article in journal (Refereed) Published
Abstract [en]

The paper examines (i) formulation of field problems of mechanics accounting for a random material microstructure and (ii) solution of associated boundary value problems. The adopted approach involves upscaling of constitutive properties according to the Hill--Mandel condition, as the only method yielding hierarchies of scale-dependent bounds and their statistics for a wide range of (non)linear elastic and inelastic, coupled-field, and even electromagnetic problems requiring (a) weakly homogeneous random fields and (b) corresponding variational principles. The upscaling leads to statistically homogeneous and isotropic mesoscale tensor random fields (TRFs) of constitutive\ properties, whose realizations are, in general, everywhere anisotropic. A summary of most general admissible correlation tensors for TRFs of ranks 1, \dots, 4 is given. A method of solving boundary value problems based on the TRF input is discussed in terms of torsion of a randomly structured rod. Given that many random materials encountered in nature (e.g., in biological and geological structures) are fractal and possess long-range correlations, we also outline a method for simulating such materials, accompanied by an application to wave propagation.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
multiscale problems, RVE, scale-dependent bounds, stochastic mechanics, tensor random fields
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-45886 (URN)10.1016/j.ijengsci.2019.103169 (DOI)2-s2.0-85074748193 ()
Available from: 2019-11-01 Created: 2019-11-01 Last updated: 2019-12-16Bibliographically approved
Malyarenko, A. & Ostoja-Starzewski, M. (2020). Towards stochastic continuum damage mechanics. International Journal of Solids and Structures, 184, 202-210
Open this publication in new window or tab >>Towards stochastic continuum damage mechanics
2020 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 184, p. 202-210Article in journal (Refereed) Published
Abstract [en]

In classical continuum damage mechanics, the distribution of cracks over differently oriented planes is an even deterministic function defined on the unit sphere. The coefficients of its Fourier expansion are completely symmetric and completely traceless tensors of even rank, the so-called fabric or damage tensors. We propose a stochastic generalisation of the above described mathematical model, where damage tensors are mean-square continuous wide-sense homogeneous and isotropic random fields.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
Tensor random field, Damage mechanics, Damage tensor, Fabric tensor
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-45222 (URN)10.1016/j.ijsolstr.2019.02.023 (DOI)
Available from: 2019-09-16 Created: 2019-09-16 Last updated: 2020-01-15
Malyarenko, A., Ni, Y., Canhanga, B. & Silvestrov, S. (2018). Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities. In: Christos H Skiadas (Ed.), Proceedings : 5th Stochastic Modeling Techniques and Data Analysis International Conference withDemographics Workshop (SMTDA2018): . Paper presented at 12 -15 June 2018, Cultural Centre of Chania, Crete, Greece (pp. 409-422). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities
2018 (English)In: Proceedings : 5th Stochastic Modeling Techniques and Data Analysis International Conference withDemographics Workshop (SMTDA2018) / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology, 2018, p. 409-422Conference paper, Published paper (Refereed)
Abstract [en]

We consider a market model with four correlated factors and two stochastic volatilities, one of which is rapid-changing, while another one is slow-changing in time. An advanced Monte Carlo methods based on the theory of cubature in Wiener space, is used to find the no-arbitrage price of the European call option in the above model.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology: , 2018
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-43299 (URN)
Conference
12 -15 June 2018, Cultural Centre of Chania, Crete, Greece
Available from: 2019-05-02 Created: 2019-05-02 Last updated: 2019-12-14Bibliographically approved
Betuel, C., Malyarenko, A., Ni, Y., Rancic, M. & Silvestrov, S. (2018). Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach. In: Christos H Skiadas (Ed.), : . Paper presented at SMTDA2018 5th Stochastic Modeling Techniques and Data Analysis International Conference - SMTDA 2018, Crete, Greece. ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach
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2018 (English)In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

The development of financial markets imposes more complex models on the option pricing problems. On the previous papers by the authors, we consider a model under which the underlying asset is driven by two independent Heston-type stochastic volatility processes of multiscale (fast and slow) mean-reverting rates and we compute an approximate solution for the option pricing problem, using asymptotic expansion method. In the present paper, we aim to calibrate the model using the market prices of options on Euro Stoxx 50 index and an equity stock in the European market. Our approach is to use the market implied volatility surface for calibrating directly a set of new parameters required in our second-order asymptotic expansion pricing formula for European options. This secondorder asymptotic expansion formula provides a better approximation formula for European option prices than the first-order formula, as explained in an earlier work of the authors.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2018
Keywords
Option pricing model, asymptotic expansion of option price, stochastic volatility model, multiscale stochastic volatility, calibration
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41091 (URN)978-618-5180-27-0 (ISBN)978-618-5180-29-4 (ISBN)
Conference
SMTDA2018 5th Stochastic Modeling Techniques and Data Analysis International Conference - SMTDA 2018, Crete, Greece
Available from: 2018-09-30 Created: 2018-09-30 Last updated: 2018-10-01Bibliographically approved
Silvestrov, S., Hössjer, O., Malyarenko, A. & Mishura, Y. (2018). Dmitrii S. Silvestrov. In: Sergei Silvestrov Anatoliy Malyarenko Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789 (pp. 1-4). Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789. Springer, 271
Open this publication in new window or tab >>Dmitrii S. Silvestrov
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov Anatoliy Malyarenko Milica Rančić, Springer, 2018, Vol. 271, p. 1-4Chapter in book (Refereed)
Abstract [en]

This chapter presents short biographical notes about Professor Dmitri S. Silvestrov.

Place, publisher, year, edition, pages
Springer, 2018
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
Keywords
Kiev University, Luleå Technical University, Mälardalen University, Stockholm University, Umeå University, Random processes, Technical universities, Stochastic systems
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41832 (URN)10.1007/978-3-030-02825-1_1 (DOI)2-s2.0-85058563975 (Scopus ID)978-3-030-02824-4 (ISBN)
Conference
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Silvestrov, S., Malyarenko, A. & Rančić, M. (2018). Preface. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 (pp. vii-x). Springer, 271
Open this publication in new window or tab >>Preface
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. vii-xChapter in book (Refereed)
Place, publisher, year, edition, pages
Springer, 2018
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41831 (URN)2-s2.0-85058576948 (Scopus ID)978-3-030-02824-4 (ISBN)978-3-030-02825-1 (ISBN)
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-01-15Bibliographically approved
Malyarenko, A. & Ostoja-Starzewski, M. (2018). Random fields related to the symmetry classes of second-order symmetric tensors. In: Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić (Ed.), Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789 (pp. 173-185). Paper presented at International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789. Springer, 271
Open this publication in new window or tab >>Random fields related to the symmetry classes of second-order symmetric tensors
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 173-185Chapter in book (Refereed)
Abstract [en]

Under the change of basis in the three-dimensional space by means of an orthogonal matrix g, a matrix A of a linear operator is transformed as A → gAg-1 Mathematically, the stationary subgroup of a symmetric matrix under the above action can be either (Formula Presented), when all three eigenvalues of A are different, or (Formula Presented), when two of them are equal, or O(3), when all three eigenvalues are equal. Physically, one typical application relates to dependent quantities like a second-order symmetric stress (or strain) tensor. Another physical setting is that of dependent fields, such as conductivity with such three cases is the conductivity (or, similarly, permittivity, or anti-plane elasticity) second-rank tensor, which can be either orthotropic, transversely isotropic, or isotropic. For each of the above symmetry classes, we consider a homogeneous random field taking values in the fixed point set of the class that is invariant with respect to the natural representation of a certain closed subgroup of the orthogonal group. Such fields may model stochastic heat conduction, electric permittivity, etc. We find the spectral expansions of the introduced random fields.

Place, publisher, year, edition, pages
Springer, 2018
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
Keywords
Random field, Spectral expansion, Symmetry class, Eigenvalues and eigenfunctions, Expansion, Heat conduction, Mathematical operators, Permittivity, Random processes, Stochastic models, Stochastic systems, Tensors, Electric permittivities, Natural representation, Random fields, Spectral expansions, Three dimensional space, Transversely isotropic, Typical application, Matrix algebra
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41836 (URN)10.1007/978-3-030-02825-1_10 (DOI)2-s2.0-85058569471 (Scopus ID)9783030028244 (ISBN)
Conference
International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications”, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 221789
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved
Malyarenko, A. (2018). Spectral expansions of random sections of homogeneous vector bundles. Theory of Probability and Mathematical Statistics, 97, 151-165
Open this publication in new window or tab >>Spectral expansions of random sections of homogeneous vector bundles
2018 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 97, p. 151-165Article in journal (Refereed) Published
Abstract [en]

Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters are described mathematically as isotropic random sections of homogeneous spin and tensor bundles. We consider the three existing approaches to rigourous construction of the above objects, emphasising an approach based on the theory of induced group representations. Both orthogonal and unitary representations are treated in a unified manner. Several examples from astrophysics are included.

Place, publisher, year, edition, pages
American Mathematical Society, 2018
Keywords
Cosmology, Random field, Vector bundle
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-43195 (URN)10.1090/tpms/1054 (DOI)2-s2.0-85064201343 (Scopus ID)
Available from: 2019-04-25 Created: 2019-04-25 Last updated: 2019-04-25Bibliographically approved
Silvestrov, S., Malyarenko, A. & Rancic, M. (Eds.). (2018). Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017. Springer
Open this publication in new window or tab >>Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017
2018 (English)Collection (editor) (Refereed)
Place, publisher, year, edition, pages
Springer, 2018. p. XIX, 475
Series
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 271
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-42245 (URN)978-3-030-02824-4 (ISBN)978-3-030-02825-1 (ISBN)
Available from: 2018-12-31 Created: 2018-12-31 Last updated: 2019-01-15Bibliographically approved
Malyarenko, A. & Ostoja-Starzewski, M. (2018). Tensor Random Fields in Continuum Mechanics. In: Altenbach, Holm and Öchsner, Andreas (Ed.), Encyclopedia of Continuum Mechanics: (pp. 1-9). Berlin, Heidelberg: Springer Berlin/Heidelberg
Open this publication in new window or tab >>Tensor Random Fields in Continuum Mechanics
2018 (English)In: Encyclopedia of Continuum Mechanics / [ed] Altenbach, Holm and Öchsner, Andreas, Berlin, Heidelberg: Springer Berlin/Heidelberg, 2018, p. 1-9Chapter in book (Refereed)
Place, publisher, year, edition, pages
Berlin, Heidelberg: Springer Berlin/Heidelberg, 2018
Keywords
Conductivity; Elasticity; Random fields; Stochastics; Uncertainty quantification
National Category
Probability Theory and Statistics Other Physics Topics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-38883 (URN)10.1007/978-3-662-53605-6_71-1 (DOI)978-3-662-53605-6 (ISBN)
Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2018-03-27Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-0139-0747

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