Skip to main content
SpringerLink
Log in

Asymptotics for the local time of a strongly dependent vector-valued Gaussian random field

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. P. Ango Nze and P. Doukhan, Non parametric minimax estimation in a weakly dependent framework,Probab. and Theor. Statist. (1996).

  2. M. Arcones,Limit theorems for non-linear functionals of a stationary Gaussian sequence of vectors, Preprint University of Utah, Salt Lake City (1993).

  3. S. M. Berman, Local times and sample function properties of stationary Gaussian processes,Trans. Amer. Math. Soc.,137 (1969), 277–299.

    Google Scholar 

  4. S. M. Berman, Local times of stochastic processes with positive definite bivariate densities.Stoch. Proc. and their Appl.,12 (1982), 1–26.

    Google Scholar 

  5. J. V. Castellana and M. R. Leadbetter, On smoothed probability density estimation for stationary processes,Stoch. Proc. and their Appl.,21 (1986), 179–193.

    Google Scholar 

  6. D. Chambers and D. Slud, Central limit theorems for non-linear functionals of stationary Gaussian processes,Prob. Th. Rel. Fields,80 (1989), 323–346.

    Google Scholar 

  7. Yu. A. Davydov, Local times for random processes,Theor. Probab. Appl.,21 (1976), 171–178.

    Google Scholar 

  8. Yu. A. Davydov, Local times for multiparameter random processes,Theor. Probab. Appl.,23 (1978), 573–583.

    Google Scholar 

  9. Yu. A. Davydov and L. Rozin, On sojourn times for functions and random processes,Theor. Probab. Appl.,23 (1978), 633–637.

    Google Scholar 

  10. R. L. Dobrushin and P. Major, Non central limit theorems for non-linear functional of Gaussian fields,Z. Wahrsch. verve. Geb.,50 (1979), 27–52.

    Google Scholar 

  11. R. Fox and M. S. Taqqu, Multiple stochastic integrals with dependent integrators,J. of Mult. Anal.,21 (1987), 105–127.

    Google Scholar 

  12. D. Geman and J. Horowitz, Occupation densities,Ann. of Probab.,8 (1980), 1–67.

    Google Scholar 

  13. M. Maejima,Sojourn of multidimensional Gaussian processes, in dependence in probability and statistics: A survey of recents result, Ed. E. Eberlein, M. Taqqu. Birkhauser, (1986), pp 91–108.

  14. M. Rosenblatt,Stochastic curve estimation, NSF-CBMS Regional Conference Series in Probability and Statistics,3. (1991).

  15. M. V. Sanchez de Naranjo, Non central limit theorems for non-linear functionals ofk Gaussian random fields,J. Mult. Anal.,44 (1993), 227–255.

    Google Scholar 

  16. G. Szegö,Orthogonal Polynomials. Amer. Math. Soc. Coll. Publ. 23 (1959).

  17. M. S. Taqqu, Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit long range dependence,Z. Wahrsch. verve. Geb.,40 (1977), 203–238.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Cergy-Pontoise, 33 Bd. du Port, 95011, Cergy Pontoise, France

    P. Doukhan

  2. Universidad Central de Venezuela and Instituto Venezolano de Investigaciones Científicas, Caracas, Venezuela

    J. R. León

Authors
  1. P. Doukhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. R. León
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was done the first author was visiting Universidad Central de Venezuela and was supported by the French and Venezuelian Ministries of Foreign Affairs.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Doukhan, P., León, J.R. Asymptotics for the local time of a strongly dependent vector-valued Gaussian random field. Acta Math Hung 70, 329–351 (1996). https://doi.org/10.1007/BF02187395

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02187395

Keywords

Search

Navigation