no. G2
Probabilités
Density estimates for the exponential functionals of fractional Brownian motion
Tien Dung, Nguyen1  ; Thu Hang, Nguyen2 ; Phuong Thuy, Pham Thi3
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, Tome 360 (2022) no. G2, 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.

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Révisé le :
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DOI : 10.5802/crmath.274
Classification : 60G22, 60H07
Tien Dung, Nguyen 1 ; Thu Hang, Nguyen 2 ; Phuong Thuy, Pham Thi 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 
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     title = {Density estimates for the exponential functionals of fractional {Brownian} motion},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {151--159},
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Tien Dung, Nguyen; Thu Hang, Nguyen; Phuong Thuy, Pham Thi. Density estimates for the exponential functionals of fractional Brownian motion. Comptes Rendus. Mathématique, Tome 360 (2022) no. G2, pp. 151-159. doi : 10.5802/crmath.274. http://www.numdam.org/articles/10.5802/crmath.274/

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