Acta Mathematica Vietnamica
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Quantitative Central Limit Theorems of Spherical Sojourn Times of Isotropic Gaussian Fields
Pham Viet Hungpp. 637-651
Abstract
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.