Comptes Rendus
no. 7
Probability theory
Kolmogorov distance between the exponential functionals of fractional Brownian motion
[Distance de Kolmogorov entre les fonctionnelles exponentielles du mouvement brownien fractionnaire]

Présenté par : Jean-François Le Gall

Nguyen Tien Dung1, 2
1 Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
2 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 629-635.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.06.009
Nguyen Tien Dung 1, 2

1 Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
2 Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam 
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Nguyen Tien Dung. Kolmogorov distance between the exponential functionals of fractional Brownian motion. Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 629-635. doi : 10.1016/j.crma.2019.06.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.06.009/

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