Comparison theorems for the small ball probabilities of Gaussian processes in weighted L₂-norms

2012/11/10 by Alexander I. Nazarov, Nazarov, Alexander I., R. S. Pusev +2
Economics, Econometrics and Finance · Mathematics · #60G15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G15

paper · pdf · doi:10.48550/arxiv.1211.2344

10 pages

arxiv created 2012/11/10 · openalex publication_date 2012/11/10 · arxiv updated 2012/11/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove comparison theorems for small ball probabilities of the Green Gaussian processes in weighted L₂-norms. We find the sharp small ball asymptotics for many classical processes under quite general assumptions on the weight.

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