Skip to main content
SpringerLink
Log in

Density estimation for continuous time processes

  • Chapter
Nonparametric Statistics for Stochastic Processes

Part of the book series: Lecture Notes in Statistics ((LNS,volume 110))

  • 426 Accesses

Abstract

In this chapter we investigate the problem of estimating density for continuons time processes when continuous or sampled data are available.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Bibliography

  1. ADLER R.J. (1990) An introduction to continuity, extrema, and Related topics for general Gaussian processes. Inst, of Math. Statist., Hayward, California.

    MATH  Google Scholar 

  2. BANON G. (1978) Nonparametric identification for diffusion processes. Siam J. Control and Optimisation V16, 380–395.

    Article  MathSciNet  Google Scholar 

  3. BANON G. and NGUYEN H.T. (1978) Sur l’estimation récurrente de la densité et de sa dérivée pour un processus de Markov, C.R. Acad. Sci. Paris t. 286, sér. A, 691–694.

    MathSciNet  MATH  Google Scholar 

  4. BANON G. and NGUYEN H.T. (1981). Recursive estimation in diffusion model. Siam J. Control and optimisation V10, 676–685.

    Google Scholar 

  5. BILLINGSLEY P. (1986). Probabihty and measure. Wiley

    Google Scholar 

  6. BOSQ D. (1993) Optimal and superoptimal quadratic error of functional estimators for continuous time processes. Preprint, Univ. Paris VI.

    Google Scholar 

  7. BOSQ D. (1995) Sur le comportement exotique de l’estimateur à noyau de la densité marginale d’un processus à temps continu. C.R. Acad. Sci. Paris t. 320, sér.I, 369–372.

    MathSciNet  MATH  Google Scholar 

  8. CASTELLANA J.V. and LEADBETTER M.R. (1986) On smoothed Probabihty density estimation for stationary processes. Stoch. Proc. Appl, 21, 179–193.

    Article  MathSciNet  MATH  Google Scholar 

  9. DELECROIX M. (1980) Sur l’estimation des densités d’un processus stationnaire à temps continu. Publ. ISUP, XXV, 1–2, 17–39.

    MathSciNet  Google Scholar 

  10. FARREL R. (1972) On the best obtainable asymptotic rates of convergence in estimation of a density function at a point. Ann. of Math. Stat. 43, 1, 170–180.

    Article  Google Scholar 

  11. IBRAGIMOV LA. and HASMINSKII R.Z. (1981) Statistical estimation — Asymptotic theory. Springer-Verlag, New-York.

    MATH  Google Scholar 

  12. IBRAGIMOV LA. and ROZANOV Y.A. (1978) Gaussian random processes. Springer Verlag, New-York.

    MATH  Google Scholar 

  13. KUTOYANTS Y.A. (1995) On density estimation by the observations of ergodic diffusion process. Preprint Un. du Maine.

    Google Scholar 

  14. LEBLANC F. (1995) PhD thesis, Univ. Paris VI.

    Google Scholar 

  15. MASRY E. (1983) Probability density estimation from sampled data. IEEE transf. inf. th. 29, 696–709.

    Article  MathSciNet  MATH  Google Scholar 

  16. MASRY E. (1988) Continuous-parameter stationary process: Statistical properties of joint density estimators, J. of mult. Anal., 26, 133–165.

    Article  MathSciNet  MATH  Google Scholar 

  17. NGUYEN H.T. (1979) Density estimation in a continuous-time stationary Markov process, Annals of Statist., 7, 2, 341–348.

    Article  MATH  Google Scholar 

  18. NGUYEN H.T. and PHAM D.T. (1980) Sur I’utilisation du temps local en Statistique des processus, C.R. Acad. Sci. Paris, 290, A, 165–170.

    MATH  Google Scholar 

  19. NGUYEN H.T. and PHAM D.T. (1981) Nonparametric estimation in diffusion model by discrete sampling.

    Google Scholar 

  20. PRASAKA RAO B.L.S. (1979) Nonparametric estimation for continuous time Markov processes via delta-families. Publ. ISUP, XXTV, 81–97.

    Google Scholar 

  21. PRASAKA RAO B.L.S. (1990) Nonparametric density estimation for stochastic process from sampled data. Publ. ISUP, XXXV, 51–84.

    Google Scholar 

  22. RAO (1992) Probability Theory. Acad. Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Statistique, Université Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris cedex 05, France

    D. Bosq

Authors
  1. D. Bosq
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Bosq, D. (1996). Density estimation for continuous time processes. In: Nonparametric Statistics for Stochastic Processes. Lecture Notes in Statistics, vol 110. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0489-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0489-0_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94713-6

  • Online ISBN: 978-1-4684-0489-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation