Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The role of the time-arrow in mean-square estimation of stochastic processes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
2018 (English)In: IEEE Control Systems Letters, ISSN 2475-1456, Vol. 2, no 1, p. 85-90Article in journal (Refereed) Published
Abstract [en]

The purpose of this letter is to point out a certain dichotomy between the information that the past and future values of a multivariate stochastic process carry about the present. More specifically, vector-valued, secondorder stochastic processes may be deterministic in one time-direction but not in the other. This phenomenon, which is absent in scalar-valued processes, is deeply rooted in the geometry of the shift-operator. The exposition and the examples we discuss are based on the work of Douglas, Shapiro, and Shields on cyclic vectors of the backward shift and relate to classical ideas going back to Wiener and Kolmogorov. We focus on rank-one stochastic processes for which we obtain an explicit characterization of all regular processes that are deterministic in the reverse timedirection. This letter builds on examples and the goal is to provide insights to a control engineering audience with interests in estimation theory and modeling of time-series.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018. Vol. 2, no 1, p. 85-90
Keywords [en]
Estimation, Linear stochastic systems
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-246530DOI: 10.1109/LCSYS.2017.2740957Scopus ID: 2-s2.0-85057636580OAI: oai:DiVA.org:kth-246530DiVA, id: diva2:1297178
Note

QC 20190319

Available from: 2019-03-19 Created: 2019-03-19 Last updated: 2019-03-19Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Karlsson, Johan

Search in DiVA

By author/editor
Karlsson, Johan
By organisation
Optimization and Systems Theory
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 2 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf