On the one-sided exit problem for fractional Brownian motion
  We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some light on the relation to the quantity $I$ studied there. 
Frank Aurzada
math.PR