Small ball properties and representation results

2015/08/28 by Yuliya Mishura, Mishura, Yuliya, Georgiy Shevchenko +1
Mathematics · #60G15 #60G22 #60H05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G15 #msc:60G22 #msc:60H05

paper · pdf · doi:10.48550/arxiv.1508.07134

arxiv created 2015/08/28 · arxiv updated 2015/08/31

Abstract

We show that small ball estimates together with Holder continuity assumption allow to obtain new representation results in models with long memory. In order to apply these results, we establish small ball probability estimates for Gaussian processes whose incremental variance admits two-sided estimates and the incremental covariance preserves sign. As a result, we obtain small ball estimates for integral transforms of Wiener processes and of fractional Brownian motion with Volterra kernels.

Related

• Small ball probabilities for a class of time-changed self-similar processes
• Small Ball Probabilities for Smooth Gaussian fields and Tensor Products of Compact Operators
• Small Ball Probabilities for the Infinite-Dimensional Ornstein-Uhlenbeck Process in Sobolev Spaces
• Comparison theorems for the small ball probabilities of Gaussian processes in weighted L₂-norms
• Log-Level Comparison Principle for Small Ball Probabilities