Path regularity of Gaussian processes via small deviations
Abstract
Description
We study the a.s. sample path regularity of Gaussian processes. To this end we relate the path regularity directly to the theory of small deviations. In particular, we show that if the process is $n$-times differentiable then the exponential rate of decay of its small deviations is at most $\varepsilon^{-1/n}$. We also show a similar result if $n$ is not an integer.
19pages
19pages