[Distance de Kolmogorov entre les fonctionnelles exponentielles du mouvement brownien fractionnaire]
Dans cette Note, nous étudions la continuité en loi relativement à l'indice de Hurst des fonctionnelles exponentielles du mouvement brownien fractionnaire. En nous reposant sur les techniques du calcul de Malliavin, nous donnons des bornes explicites de la distance de Kolmogorov entre deux fonctionnelles d'indices de Hurst différents.
In this note, we investigate the continuity in law with respect to the Hurst index of the exponential functional of the fractional Brownian motion. Based on the techniques of Malliavin's calculus, we provide an explicit bound on the Kolmogorov distance between two functionals with different Hurst indexes.
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@article{CRMATH_2019__357_7_629_0,
author = {Dung, Nguyen Tien},
title = {Kolmogorov distance between the exponential functionals of fractional {Brownian} motion},
journal = {Comptes Rendus. Math\'ematique},
pages = {629--635},
publisher = {Elsevier},
volume = {357},
number = {7},
year = {2019},
doi = {10.1016/j.crma.2019.06.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.06.009/}
}
TY - JOUR AU - Dung, Nguyen Tien TI - Kolmogorov distance between the exponential functionals of fractional Brownian motion JO - Comptes Rendus. Mathématique PY - 2019 SP - 629 EP - 635 VL - 357 IS - 7 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.06.009/ DO - 10.1016/j.crma.2019.06.009 LA - en ID - CRMATH_2019__357_7_629_0 ER -
%0 Journal Article %A Dung, Nguyen Tien %T Kolmogorov distance between the exponential functionals of fractional Brownian motion %J Comptes Rendus. Mathématique %D 2019 %P 629-635 %V 357 %N 7 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.06.009/ %R 10.1016/j.crma.2019.06.009 %G en %F CRMATH_2019__357_7_629_0
Dung, Nguyen Tien. Kolmogorov distance between the exponential functionals of fractional Brownian motion. Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 629-635. doi : 10.1016/j.crma.2019.06.009. http://www.numdam.org/articles/10.1016/j.crma.2019.06.009/
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