Density estimates for the exponential functionals of fractional Brownian motion

Nguyen Tien Dung; Nguyen Thu Hang; Pham Thi Phuong Thuy

doi:10.5802/crmath.274

Probabilités

Density estimates for the exponential functionals of fractional Brownian motion

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

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 151-159.

Résumé

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.

Reçu le : 2021-03-06
Révisé le : 2021-06-19
Accepté le : 2021-09-21
Publié le : 2022-02-15

DOI : 10.5802/crmath.274

Classification : 60G22, 60H07

Affiliations des auteurs :

Nguyen Tien Dung ¹ ; Nguyen Thu Hang ² ; Pham Thi Phuong Thuy ³

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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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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