Small ball properties and representation results

Yuliya Mishura and Georgiy Shevchenko

Stochastic Processes and their Applications, 2017, vol. 127, issue 1, 20-36

Abstract: 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.

Keywords: Integral representation; Generalized Lebesgue–Stieltjes integral; Small ball estimate; Quasi-helix; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2016.05.007

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