Acta Mathematica Vietnamica

, Volume 42, Issue 4, pp 637–651 | Cite as

Quantitative Central Limit Theorems of Spherical Sojourn Times of Isotropic Gaussian Fields

  • Pham Viet HungEmail author


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.


Sojourn 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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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Institute of Mathematics, Vietnam Academy of Science and Technology (VAST)HanoiVietnam

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