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

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Published: Mar 30, 2015
Keywords:
Malliavin calculus, Kolmogorov distance, Stein’s method, multidimensional normal approximation, Wasserstein distance, fractional Brownian motion.
Mathematics Subject Classification:
Stein’s method, 60H07.

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Yoon Tae Kim
Department of Finance and Information Statistics Hallym University Chunchon 200-702, Korea
Hyun Suk Park
Department of Finance and Information Statistics Hallym University Chunchon 200-702, Korea

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].



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Supporting Agencies

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).

References

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