Extremes of a certain class of Gaussian processes

We consider the extreme values of fractional Brownian motions, self-similar Gaussian processes and more general Gaussian processes which have a trend −ctβ for some constants c,β>0 and a variance t2H. We derive the tail behaviour of these extremes and show that they occur mainly in the neighbourhood of the unique point t0 where the related boundary function (u+ctβ)/tH is minimal. We consider the case that H<β.