Probability of Large Deviations of the Power of a Stationary Gaussian Process

The asymptotic behavior of the probability function $P_T=P(\int^T_0\xi^2(t)dt>TR(0)x_T)$ is investigated, where $\xi(t)$ is a stationary Gaussian process with expectation $E\xi(t)=0$ and correlation function $R(t)$.