Exponential tightness for Gaussian processes, with applications to some sequences of weighted means

Exponential tightness plays a crucial role in large deviations; in fact this condition is often required to obtain the large deviation principle for a sequence of random variables taking values on an infinite dimensional topological space. In this paper we present some conditions which yield the exponential tightness of a sequence of continuous Gaussian processes. Moreover we check these conditions for some sequences of weighted means.