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http://dx.doi.org/10.11568/kjm.2015.23.1.1

KOLMOGOROV DISTANCE FOR MULTIVARIATE NORMAL APPROXIMATION  

Kim, Yoon Tae (Department of Finance and Information Statistics Hallym University)
Park, Hyun Suk (Department of Finance and Information Statistics Hallym University)
Publication Information
Korean Journal of Mathematics / v.23, no.1, 2015 , pp. 1-10 More about this Journal
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$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].
Keywords
Malliavin calculus; Kolmogorov distance; Stein's method; multidimensional normal approximation; Wasserstein distance; fractional Brownian motion;
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1 Bhattacharya, R. N. and Ranga Rao. R (1986). Normal Approximation and Asymptotic Expansion. Krieger, Melbourne, FL.
2 Breuer, P and Major, P. (1983). Central limit theorems for nonlinear functionals of Gaussian fieds, J. Multivariate Analysis, 13 (3), 425-441.   DOI
3 Chen, L and Shao, Q.-M. (2005). Stein's method for normal approximation, in: An Introduction to Stein's method, in Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., vol. 4, Singapore Univ. Press, Singapore, 1-59.
4 Giraitis, L and Surgailis, D. (1985). CLT and other limit theorems for functionals of Gaussian processes, Z. Wahrscheinlichkeitstheor. Verwandte Geb., 70 (3), 191-212.   DOI
5 Gotze, F.(2009). On the rate of convergence in the multivariate CLT, Ann. Probab., 19, 724-739.
6 Nourdin, I. and Peccati, G. (2009). Stein's method on Wiener Chaos, Probab.Theory Related Fields, 145, 75-118.   DOI
7 Nourdin, I. and Peccati, G.(2009). Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields, Annals of Probab., 37 (6), 2231-2261.   DOI   ScienceOn
8 Nourdin, I. and Peccati, G and Podolskij, M. (2011). Quantitative Breuer-Major theorems, Stochasic rocesses and their Applicatrions, 121, 793-812.   DOI   ScienceOn
9 Nourdin, I. and Peccati, G and Reveillac, A. (2010). Multivariate normal approximation using Stein's method and Malliavin calculus, Ann. Inst. H. Poincare(B) Probab.Statist., 46 (1), 45-98.   DOI   ScienceOn
10 D. Nualart (2006), Malliavin calculus and related topics, 2nd Ed. Springer.