Spectral expansions of homogeneous and isotropic tensor-valued random fields

Anatoliy Malyarenko, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number59
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number3
StatePublished - Jun 1 2016


  • Random field
  • Spectral expansion
  • Tensor random fields

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


Dive into the research topics of 'Spectral expansions of homogeneous and isotropic tensor-valued random fields'. Together they form a unique fingerprint.

Cite this