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CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields

Author

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  • Marie Kratz

    (ESSEC Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique)

  • Sreekar Vadlamani

    (TIFR-CAM - Center for Applicable Mathematics [Bangalore] - TIFR - Tata Institute for Fundamental Research)

Abstract

Our interest in this paper is to explore limit theorems for various geometric function-als of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times (see [4, 13, 14, 18, 22, 25] for a sample of works in such settings). The most recent addition being [6] where a central limit theorem (CLT) for Euler-Poincaré characteristic of the excursions set of a Gaussian random field is proven under appropriate conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz-Killing curvatures of excursion sets of Gaussian random fields in an appropriate setting.

Suggested Citation

  • Marie Kratz & Sreekar Vadlamani, 2016. "CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields," Working Papers hal-01373091, HAL.
    • Handle: RePEc:hal:wpaper:hal-01373091
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01373091
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    References listed on IDEAS

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    1. Nourdin, Ivan & Peccati, Giovanni & Podolskij, Mark, 2011. "Quantitative Breuer-Major theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 793-812, April.
    2. 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.
    3. Pham, Viet-Hung, 2013. "On the rate of convergence for central limit theorems of sojourn times of Gaussian fields," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2158-2174.
    4. Meschenmoser, D. & Shashkin, A., 2011. "Functional central limit theorem for the volume of excursion sets generated by associated random fields," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 642-646, June.
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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.

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    More about this item

    Keywords

    excursion sets; Lipschitz-Killing curvatures; chaos expansion; Gaussian fields; CLT;
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