Explicit computation of second-order moments of importance sampling estimators for fractional Brownian motion

We study a family of importance sampling estimators of the probability of level crossing when the crossing level is large or the intensity of the noise is small. We develop a method which gives, explicitly the asymptotics of the second-order moment. Some of the results apply to fractional Brownian motion, some are more general. The main tools are refined versions of classical large-deviations results.