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

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

2010-09-07

arxiv.org/abs/1009.1252v1

Mathematics

Spectral Theory

15 pages, 1 figure

Scientific paper

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.

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