Abstract
We establish lower and upper bounds for the small ball probability of a centered Gaussian process(X(t)) t∈[0,1] N under Hölder-type norms as well as upper bounds for some more general functionals. This extends recently established results for the uniform norm. In addition, our proof of the lower bound is considerably simpler. In the special caseN=1 we establish precise estimates under a wider class of norms including in particular the Besov norms.
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Stolz, W. Some small ball probabilities for Gaussian processes under nonuniform norms. J Theor Probab 9, 613–630 (1996). https://doi.org/10.1007/BF02214078
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DOI: https://doi.org/10.1007/BF02214078