Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes

Abstract

We find the logarithmic small ball asymptotics for the $L_2$-norm with respect to a degenerate self-similar measures of a certain class of Gaussian processes including Brownian motion, Ornstein - Uhlenbeck process and their integrated counterparts.Comment: 15 pages, 1 figur