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Our aim in this article is to provide explicit computable estimates for thecumulative distribution function (c.d.f.) and the $p$-th order moment of theexponential functional of a fractional Brownian motion (fBM) with drift. Usingelementary techniques, we prove general upper bounds for the c.d.f. ofexponential functionals of continuous Gaussian processes. On the other hand, byapplying classical results for extremes of Gaussian processes, we derivegeneral lower bounds. We also find estimates for the $p$-th order moment andthe moment-generating function of such functionals. As a consequence, we obtainexplicit lower and upper bounds for the c.d.f. and the $p$-th order moment ofthe exponential functionals of a fBM, and of a series of independent fBMs. Inaddition, we show the continuity in law of the exponential functional of a fBMwith respect to the Hurst parameter.

Estimates for exponential functionals of continuous Gaussian processes with emphasis on fractional Brownian motion