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

Open this publication in new window or tab >>RVE problem: mathematical aspects and related stochastic mechanics### Karimi, Pouyan

### Malyarenko, Anatoliy

### Ostoja-Starzewski, Martin

### Zhang, Xian

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2019-11-01 Created: 2019-11-01 Last updated: 2019-12-16Bibliographically approved

University of Illinois at Urbana-Champaigne, USA.

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

University of Illinois at Urbana-Champaign, USA.

University of Illinois at Urbana-Champaigne, USA.

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.

Open this publication in new window or tab >>Towards stochastic continuum damage mechanics### Malyarenko, Anatoliy

### Ostoja-Starzewski, Martin

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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Available from: 2019-09-16 Created: 2019-09-16 Last updated: 2020-01-15

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

University of Illinois at Urbana-Champaign, USA.

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.

Open this publication in new window or tab >>Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities### Malyarenko, Anatoliy

### Ni, Ying

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

### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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
#####

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Available from: 2019-05-02 Created: 2019-05-02 Last updated: 2019-12-14Bibliographically approved

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

Faculty of Sciences, Department of Mathematics and Computer Sciences,Eduardo Mondlane University, Box 257, Maputo, Mozambique.

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.

Open this publication in new window or tab >>Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach### Betuel, Canhanga

### 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.### Rancic, Milica

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); ### Silvestrov, Sergei

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_3_j_idt188_j_idt202",{id:"formSmash:j_idt184:3:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 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]

##### 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
#####

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Available from: 2018-09-30 Created: 2018-09-30 Last updated: 2018-10-01Bibliographically approved

Faculty of Sciences, Dept of Mathematics and Computer Sciences, Eduardo Mondlane University, Mozambique.

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.

Open this publication in new window or tab >>Dmitrii S. Silvestrov### Silvestrov, Sergei

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

### Malyarenko, Anatoliy

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

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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
#####

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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

Department of Mathematics, Stockholm University, Sweden.

Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine.

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

Open this publication in new window or tab >>Preface### Silvestrov, Sergei

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.### Rančić, Milica

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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)
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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-01-15Bibliographically approved

Open this publication in new window or tab >>Random fields related to the symmetry classes of second-order symmetric tensors### Malyarenko, Anatoliy

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Ostoja-Starzewski, M.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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]

##### 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
#####

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Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2018-12-31Bibliographically approved

University of Illinois at Urbana-Champaign, Urbana, United States.

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.

Open this publication in new window or tab >>Spectral expansions of random sections of homogeneous vector bundles### Malyarenko, Anatoliy

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 97, p. 151-165Article in journal (Refereed) Published
##### Abstract [en]

##### 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)
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Available from: 2019-04-25 Created: 2019-04-25 Last updated: 2019-04-25Bibliographically approved

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.

Open this publication in new window or tab >>Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017### Silvestrov, Sergei

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.### Rancic, Milica

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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)
#####

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Available from: 2018-12-31 Created: 2018-12-31 Last updated: 2019-01-15Bibliographically approved

Open this publication in new window or tab >>Tensor Random Fields in Continuum Mechanics### Malyarenko, Anatoliy

Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.### Ostoja-Starzewski, Martin

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##### 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)
#####

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Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2018-03-27Bibliographically approved

University of Illinois at Urbana-Champaign.