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.
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.
Accepted:
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Nguyen Tien Dung 1, 2
@article{CRMATH_2019__357_7_629_0, author = {Nguyen Tien Dung}, 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}, }
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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