Comparison theorems for the small ball probabilities of Gaussian processes in weighted $L_2$-norms

Alexander I. Nazarov; Ruslan S. Pusev

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arXiv · 1211.2344

Comparison theorems for the small ball probabilities of Gaussian processes in weighted $L_2$-norms

Alexander I. Nazarov·Ruslan S. Pusev

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Abstract

We prove comparison theorems for small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms. We find the sharp small ball asymptotics for many classical processes under quite general assumptions on the weight.

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Alexander I. Nazarov, Ruslan S. Pusev. 2012-11-10. Comparison theorems for the small ball probabilities of Gaussian processes in weighted $L_2$-norms. https://arxiv.org/abs/1211.2344

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