Translator Disclaimer
February 2015 Integrability and concentration of the truncated variation for the sample paths of fractional Brownian motions, diffusions and Lévy processes
Witold Marek Bednorz, RafaŁ Marcin Ł ochowski
Bernoulli 21(1): 437-464 (February 2015). DOI: 10.3150/13-BEJ574

Abstract

For a real càdlàg function $f$ defined on a compact interval, its truncated variation at the level $c>0$ is the infimum of total variations of functions uniformly approximating $f$ with accuracy $c/2$ and (in opposite to the total variation) is always finite. In this paper, we discuss exponential integrability and concentration properties of the truncated variation of fractional Brownian motions, diffusions and Lévy processes. We develop a special technique based on chaining approach and using it we prove Gaussian concentration of the truncated variation for certain class of diffusions. Further, we give sufficient and necessary condition for the existence of exponential moment of order $\alpha>0$ of truncated variation of Lévy process in terms of its Lévy triplet.

Citation

Download Citation

Witold Marek Bednorz. RafaŁ Marcin Ł ochowski. "Integrability and concentration of the truncated variation for the sample paths of fractional Brownian motions, diffusions and Lévy processes." Bernoulli 21 (1) 437 - 464, February 2015. https://doi.org/10.3150/13-BEJ574

Information

Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 1318.60041
MathSciNet: MR3322326
Digital Object Identifier: 10.3150/13-BEJ574

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.21 • No. 1 • February 2015
Back to Top