Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Problèmes de prediction pour le processus de Wiener a deux parametres
Download PDF
Download PDF
  • Published: July 1986

Problèmes de prediction pour le processus de Wiener a deux parametres

  • L. Carraro1 

Probability Theory and Related Fields volume 72, pages 619–635 (1986)Cite this article

  • 57 Accesses

  • 4 Citations

  • Metrics details

Summary

We give a decomposition of the two-parameter real Wiener process (W(x, y), (x, y)∈(ℝ+)2 by using the Fourier transform defined on the group which leave it invariant. Then we use this decomposition to obtain some prediction results for this process, which allow us to give upper and lower bounds for the correlation coefficient of the vector-spaces respectively generated by the two families {W(x, y), xy ε≦s} and {W(x, y), xy ε≧t}, 0s t, ε∈{-1,1}.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Bibliographie

  1. Carraro, L.: Un théorème de prédiction pour le processus de Wiener à deux paramètres. C.R. Acad. Sci., Paris, à paraître

  2. Czőrgő, M., Révész, P.: Strong approximations in probability and statistics. New York: Academic Press 1981

    Google Scholar 

  3. Dym, H., McKean, H.P.: Gaussian processes, function theory and the inverse spectral problem. New York: Academic Press 1976

    Google Scholar 

  4. Ehm, W.: Sample function properties of multi-parameter stable processes. Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 195–228 (1981)

    Google Scholar 

  5. Goldman, A.: Estimations analytiques concernant le mouvement brownien fractionnaire à plusieurs paramètres. C.R. Acad. Sci. Paris 298, 91–93 (1984)

    Google Scholar 

  6. Goldman, A.: La mesure de Hausdorff des trajectoires du mouvement brownien à plusieurs paramètres. C.R. Acad. Sci., Paris 300, 643–645 (1985)

    Google Scholar 

  7. Kahane, J.P.: Recent progress in Fourier analysis. Proceedings of the Seminar on Fourier analysis held in E.I. Escorial, Spain, June 30–July 5 (1983)

  8. McKean, H.P.: Brownian motion with several-dimensional time. Theory Probab. Appl. 8, 335–354 (1963)

    Google Scholar 

  9. Orey, S., Pruitt, W.E.: Sample functions of the N-parameter Wiener process. Ann. Probab. 1, 138–163 (1973)

    Google Scholar 

  10. Pitt, L.D.: Local time for gaussian vector fields. Indiana Univ. Math. J. 27, 309–330 (1978)

    Google Scholar 

  11. Schoenberg, I.J.: On certain metric spaces arising from euclidean spaces by a change of metric and their imbedding in Hilbert space. Ann. Math. 38, 787–793 (1937)

    Google Scholar 

  12. Wong, E., Zakai, M.: Differentiations formulas for stochastic integrals in the plane. Stochastic Processes Appl. 6, 339–349 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, 43, Université Claude Bernard-Lyon 1, bd du 11 novembre 1918, F-69622, Villeurbanne Cedex, France

    L. Carraro

Authors
  1. L. Carraro
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Carraro, L. Problèmes de prediction pour le processus de Wiener a deux parametres. Probab. Th. Rel. Fields 72, 619–635 (1986). https://doi.org/10.1007/BF00344724

Download citation

  • Received: 09 August 1985

  • Issue Date: July 1986

  • DOI: https://doi.org/10.1007/BF00344724

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature