Path regularity of Gaussian processes via small deviations

• Autorzy: Aurzada F.
• Języki publikacji: EN

Abstrakty

EN

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 ε^-1/n. We also show a similar result if n is not an integer. Further generalizations are given, which parallel the entropy method to determine the small deviations. In particular, the present approach seems to be a probabilistic interpretation of the multiplicativity property of the entropy numbers.

Słowa kluczowe

EN

small deviation; small-ball probability; Gaussian process; sample path regularity

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2011
• Tom: Vol. 31, Fasc. 1
• Strony: 61--78
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Aurzada F.

• Technische Universität Berlin, Sekr. MA7-5, Straße des 17. Juni 136, 10623 Berlin, Germany

Bibliografia

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