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Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields

Author

Listed:
  • Marie F. Kratz

    (Université Paris I & U.F.R. de Mathématiques et Informatique, Université René Descartes, Paris V)

  • José R. León

    (Universidad Central de Venezuela)

Abstract

We introduce a general method, which combines the one developed by authors in 1997 and one derived from the work of Malevich,(17) Cuzick(7) and mainly Berman,(3) to provide in an easy way a CLT for level functionals of a Gaussian process, as well as a CLT for the length of a level curve of a Gaussian field.

Suggested Citation

  • Marie F. Kratz & José R. León, 2001. "Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields," Journal of Theoretical Probability, Springer, vol. 14(3), pages 639-672, July.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:3:d:10.1023_a:1017588905727
    DOI: 10.1023/A:1017588905727
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    References listed on IDEAS

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    1. Kratz, Marie F. & León, JoséR., 1997. "Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 237-252, March.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
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    Cited by:

    1. Shevchenko, Radomyra & Todino, Anna Paola, 2023. "Asymptotic behaviour of level sets of needlet random fields," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 268-318.
    2. Marie Kratz & Sreekar Vadlamani, 2018. "Central Limit Theorem for Lipschitz–Killing Curvatures of Excursion Sets of Gaussian Random Fields," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1729-1758, September.
    3. Tudor, Ciprian A. & Zurcher, Jérémy, 2024. "The spatial sojourn time for the solution to the wave equation with moving time: Central and non-central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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