A note on LDP for supremum of Gaussian processes over infinite horizon

The aim of this paper is to give a short proof of a large deviation result for supremum of nencentered Gaussian process over infinite horizon. We study family {[mu]X,d;u; u>0} of Borel probability measures on , wherefor Borel , drift function d(t) and centered Gaussian processes {X(t); t[greater-or-equal, slanted]0} with variance function [sigma]2(t). We assume that for each 0<[var epsilon][less-than-or-equals, slant]1We obtain logarithmic asymptotic of . Under additional assumption, that [sigma]2(t) is regularly varying at [infinity] and d(t) is linear, we prove large deviation principle for {[mu]X,d;u; u>0}.