Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$

We prove several results on exact asymptotic formulas for small deviations in the $L^p$-norm with $2\le p\le\infty$ for Bogoliubov's stationary Gaussian process $\xi(t)$. We prove the property of mutual absolute continuity for the conditional Bogoliubov measure and the conditional Wiener measure and calculate the Radon–Nikodym derivative.