Path regularity of Gaussian processes via small deviations

Details Path regularity of Gaussian processes via small deviations Path regularity of Gaussian processes via small deviations

2009-05-20

arxiv.org/abs/0905.3358v1

Mathematics

Probability

19pages

Scientific paper

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.

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