Small ball properties and representation results
Probability
2015-08-31 v1
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.
Keywords
Cite
@article{arxiv.1508.07134,
title = {Small ball properties and representation results},
author = {Yuliya Mishura and Georgiy Shevchenko},
journal= {arXiv preprint arXiv:1508.07134},
year = {2015}
}