Path regularity of Gaussian processes via small deviations - Mathematics > Probability

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Abstract: We study the a.s. sample path regularity of Gaussian processes. To this endwe relate the path regularity directly to the theory of small deviations. Inparticular, we show that if the process is $n$-times differentiable then theexponential 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.