Korean J. Math.  Vol 23, No 1 (2015)  pp.1-10
DOI: https://doi.org/10.11568/kjm.2015.23.1.1

Kolmogorov distance for Multivariate normal approximation

Yoon Tae Kim, Hyun Suk Park

Abstract


This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields.  The aim of the present work is to derive  explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance  studied by  Nourdin et al. Ann. Inst. H. Poincar\'{e}(B) Probab.Statist. 46(1) (2010) 45-98].


Keywords


Malliavin calculus, Kolmogorov distance, Stein’s method, multidimensional normal approximation, Wasserstein distance, fractional Brownian motion.

Subject classification

60H07.

Sponsor(s)

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A4A01012783 and NRF-2013R1A1A2008478).

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References


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