An application of the Neyman–Oearson lemma to Gaussian processes

Let $\xi(t)$, $i=1,2$, $t\in[0,1]$, be Gaussian zero mean processes with continuous sample paths. Bounds for the probabilities
$$ \beta_i=\mathsf P\{\xi_i(t)-a_i(t)\in B\},\qquad i=1,2, $$
are given, where $a_i\in C[0,1]$ and $B$ is a Borel subset of $C[0,1]$. Bibliography: 5 titles.