title: On a decomposition of additive random fields
metadata.name: dc.contributor.author
metadata.value: Zani, Marguerite
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Khartov, Alexey A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-04-10T12:24:37Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:24:37Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zani M., Khartov A.A. On a decomposition of additive random fields. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 39–49.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.104
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17326
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider an additive random field on [0, 1]d, which is a sum of d uncorrelated random
  processes. We assume that the processes have zero mean and the same continuous covariance
  function. There is a significant interest in the study of random fields of this type.
  They appear for example in the theory of intersections and selfintersections of Brownian
  processes, in the problems concerning the small ball probabilities, and in the finite rank
  approximation problems with arbitrary large parametric dimension d. In the last problems
  the spectral characteristics of the covariance operator play key role. For a given additive random field the eigenvalues of its covariance operator easily depend on the eigenvalues of
  the covariance operator of the marginal processes in the case, when the latter has identical
  1 as an eigenvector. In the opposite case the dependence is complex, that makes these random
  fields difficult to study. Here decomposing the random field into the sum of its integral
  and its centered version, the summands will be orthogonal in L2([0, 1]d), but in the general
  case they are correlated. In the present paper we propose another interesting decomposition
  for the random field, that was observed by the authors within finite rank approximation
  problems in the average case setting. In the derived decomposition the summands are orthogonal
  in L2([0, 1]d) and uncorrelated. Moreover, for large d they are respectively close
  to the integral and to the centered version of the random field with small relative mean
  squared error.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by St. Petersburg State University (grant SPbSU–DFG 6.65.37.2017).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: additive random fields
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: decomposition
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: covariance function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: covariance operator
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: eigenpairs
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: average case approximation complexity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a decomposition of additive random fields
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 39-49.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17326/1/39-49.pdf
resources.format: Adobe PDF
resources.size: 321,4 kB