The Small Ball Asymptotics in Hilbert Norm for the Kac--Kiefer--Wolfowitz Processes

We consider the problem of a small ball behavior in L-2-norm for some Gaussian processes of statistical interest. The problem is reduced to the spectral asymptotics for some integral-differential operators. To find these asymptotics we construct complete asymptotic expansions of some oscillation integrals with slowly varying amplitudes.