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Spectral expansions of homogeneous and isotropic tensor-valued random fields
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-0139-0747
University of Illinois at Urbana-Champaign.
2016 (English)In: Zeitschrift für angewandte Matematik und Physik ZAMP, ISSN 1420-9039, Vol. 67, no 3, 59Article in journal (Refereed) Published
Abstract [en]

We establish spectral expansions of tensor-valued homogeneous and isotropic random fields in terms of stochastic integrals with respect to orthogonal scattered random measures previously known only for the case of tensor rank 0. The fields under consideration take values in the 3-dimensional Euclidean space E3 and in the space S2(E3) of symmetric rank 2 tensors over E3. We find a link between the theory of random fields and the theory of finite-dimensional convex compact sets. These random fields furnish stepping-stone for models of rank 1 and rank 2 tensor-valued fields in continuum physics, such as displacement, velocity, stress, strain, providing appropriate conditions (such as the governing equation or positive-definiteness) are imposed.

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2016. Vol. 67, no 3, 59
Keyword [en]
Random field · Tensor random fields · Spectral expansion
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-31534DOI: 10.1007/s00033-016-0657-8ISI: 000378940400025Scopus ID: 2-s2.0-84965122349OAI: oai:DiVA.org:mdh-31534DiVA: diva2:926453
Available from: 2016-05-06 Created: 2016-05-06 Last updated: 2016-10-16Bibliographically approved

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Publisher's full textScopushttp://download.springer.com/static/pdf/38/art%253A10.1007%252Fs00033-016-0657-8.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00033-016-0657-8&token2=exp=1462547031~acl=%2Fstatic%2Fpdf%2F38%2Fart%25253A10.1007%25252Fs00033-016-0657-8.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs00033-016-0657-8*~hmac=8581c057a35d2f59d2adf8fb643c028c187669839147e967eec2a98122e7afd7

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
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Language
  • de-DE
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Output format
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