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On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

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  • Pham, Viet-Hung

Abstract

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2158-2174
    DOI: 10.1016/j.spa.2013.01.016
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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414913000355
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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.
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    Cited by:

    1. Marie Kratz & Sreekar Vadlamani, 2016. "CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields," Working Papers hal-01373091, HAL.

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