Quantitative Central Limit Theorems of Spherical Sojourn Times of Isotropic Gaussian Fields
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We investigate the rate of convergence for the central limit theorems of sojourn times on the growing sphere of isotropic Gaussian fields defined on the whole Euclidean space. In the case of the sojourn times defined on a cube, the similar problem has been studied by using the Malliavin-Stein method. Following this idea, in this paper, we establish the explicit rate for various probability distances with a careful examination of the variance.
KeywordsSojourn time Isotropic Gaussian field Malliavin-Stein method
Mathematics Subject Classification (2010)Primary 60H07 Secondary 60F05 60D05
This work is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2014.14. We would like to thank the anonymous referee for his meticulous and rigorous reading of the manuscript and his numerous suggestions that greatly improve the presentation of the present paper.
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