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.

15 pages, 1 figure

References in corpus (1)

• Asymptotics of eigenvalues of Sturm--Liouville problem with discrete self-similar weight

Cited by in corpus (1)

• $L_2$-small ball asymptotics for Gaussian random functions: a survey