A strong limit theorem for Gaussian processes

We demonstrate here a similar result for a large class of Gaussian processes including the Wiener process as a particular case. Notation: in the following { X(t), 0? t <1 } will denote a Gaussian stochastic process of real-valued random variables with mean function E { X(t) =m(t) and covariance function E{X(s)X(t) } -m(s)m(t) =r(s, t). Now assume that m (t) has a bounded first derivative for 0< t ?1. Furthermore, assume that r(s, t) is continuous in 0 <s, t <1 and has uniformly bounded second derivatives for s 5t. Let