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Digitale Medien

Some small ball probabilities for Gaussian processes under nonuniform norms (1996)

Stolz, Wolfgang

Springer

Journal of theoretical probability 9 (1996), S. 613-630

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ISSN: 1572-9230

Schlagwort(e): Small ball estimates ; fractional Brownian motion ; Hölder-type norms ; Besov norms

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02214078

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