Comptes Rendus
Probability theory
Density estimates for the exponential functionals of fractional Brownian motion
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 151-159.

In this note, we investigate the density of the exponential functional of the fractional Brownian motion. Based on the techniques of Malliavin’s calculus, we provide a log-normal upper bound for the density.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.274
Classification: 60G22, 60H07
Nguyen Tien Dung 1; Nguyen Thu Hang 2; Pham Thi Phuong Thuy 3

1 Department of Mathematics, VNU University of Science, Vietnam, National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, 084 Vietnam
2 Department of Mathematics, Hanoi University of Mining and Geology, 18 Pho Vien, Bac Tu Liem, Hanoi, 084 Vietnam
3 The faculty of Basic Sciences, Vietnam Air Defence and Air Force Academy, Son Tay, Ha Noi, 084 Vietnam
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     author = {Nguyen Tien Dung and Nguyen Thu Hang and Pham Thi Phuong Thuy},
     title = {Density estimates for the exponential functionals of fractional {Brownian} motion},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {151--159},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.274},
     language = {en},
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Nguyen Tien Dung; Nguyen Thu Hang; Pham Thi Phuong Thuy. Density estimates for the exponential functionals of fractional Brownian motion. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 151-159. doi : 10.5802/crmath.274. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.274/

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