Skip to main content

Recent Results on Random and Spectral Measures with Some Applications in Statistics

  • Conference paper
Functional and Operatorial Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

  • 1963 Accesses

In this talk we define and study first the convolution product of two spectral measures and secondly the tensor and convolution products of random measures. Then we propose some applications in stationary processes statistics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Azencott R., Dacunha-Castelle D.: Séries d'observations irrégulières. Modélisation et prévision. Techniques Stochastiques, Masson (1984).

    Google Scholar 

  2. Birman M., Solomjak M.: Tensor product of a nite number of spectral measures is always a spectral measure. Integ. Eq. Oper. Th. 24, 179-187 (1996).

    Article  MATH  Google Scholar 

  3. Benchikh T., Boudou A., Romain Y.: Mesures aléatoires opératorielle et banachique. Application aux séries stationnaires. C.R. Acad. Sci. Paris. SérieI, Math. 345, 345-348 (2007).

    MATH  MathSciNet  Google Scholar 

  4. Boudou A.: Interpolation de processus stationnaires. C.R. Acad. Sci. Paris, SérieI, Math. 33, 12, 1021-1024 (2003).

    MathSciNet  Google Scholar 

  5. Boudou A.: Groupe d'opérateurs unitaires déduit d'une mesure spectrale - une ap-plication. C.R. Acad. Sci. Paris. SerieI, Math., 344, 12, 791-794 (2007).

    MATH  MathSciNet  Google Scholar 

  6. Boudou A., Dauxois J.: Principal component analysis for a stationary random func-tion de ned on a locally compact abelian group. J. Multivariate Anal. 51, no. 1, 1-16 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  7. Boudou A., Romain Y.: On spectral and random measures associated to continuous and discrete time processes. Stat. Proba. Letters. 59, 145-157 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. Boudou A., Romain Y.: Sur l'intégrale par rapport à une mesure aléatoire tensorielle et ses applications aux processus stationnaires multidimensionnels. Publi. Labo. Stat. Proba., 08-05, 1-27, Univ. P. Sabatier, Toulouse. (2005).

    Google Scholar 

  9. Dauxois J., Romain Y., Viguier S.: Tensor products and statistics. Lin. Alg. Appl. 210, 59-88 (1994).

    Article  MATH  Google Scholar 

  10. Halmos, P.R. Introduction to Hilbert space and theory of spectral multiplicity. Reprint of the second (1957) edition. AMS Chelsea Publishing, Providence, RI (1998).

    MATH  Google Scholar 

  11. Riesz F., Nagy B.SZ.: Leçons d'analyse fonctionnelle. Gauthiers-Villars, Paris (1968).

    Google Scholar 

  12. Schae er H.H.: Banach lattices and positive operators. Springer-Verlag, Berlin Hei-delberg New York (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Physica-Verlag Heidelberg

About this paper

Cite this paper

Boudou, A., Cabral, E., Romain, Y. (2008). Recent Results on Random and Spectral Measures with Some Applications in Statistics. In: Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2062-1_13

Download citation

Publish with us

Policies and ethics