On supremum of one-point conditioned fractional Brownian motion (Q2723986)

The asymptotic behavior of probabilities of maximal value for non-centered Gaussian processes is considered. The main assumption is that the variance of the process attains its maximum at a single point. The authors use the double sum method and extend some previous results of the first author. Finally the asymptotic behavior of the conditional probability for fractional Brownian motion is obtained as a consequence of the theorem proved in the paper.