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math.PR2021
Density estimates for the exponential functionals of fractional Brownian motion
Nguyen Tien Dung, Nguyen Thu Hang, Pham Thi Phuong Thuy
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 u…
math.PR2021
On the density of nonlinear statistics
Nguyen Tien Dung
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and su…