Small ball properties and representation results

We show that small ball estimates together with Hölder 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 estima...

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Bibliographic Details
Published in:	Stochastic processes and their applications Vol. 127; no. 1; pp. 20 - 36
Main Authors:	Mishura, Yuliya, Shevchenko, Georgiy
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-01-2017
Subjects:	Fractional Brownian motion Generalized Lebesgue–Stieltjes integral Integral representation Quasi-helix Small ball estimate Generalized Lebesgue–Stieltjes integral 60G22 Quasi-helix Small ball estimate 60H05 Integral representation Fractional Brownian motion 60G15
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Summary:	We show that small ball estimates together with Hölder 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.
ISSN:	0304-4149 1879-209X
DOI:	10.1016/j.spa.2016.05.007