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November 2007 Sample path properties of bifractional Brownian motion
Ciprian A. Tudor, Yimin Xiao
Bernoulli 13(4): 1023-1052 (November 2007). DOI: 10.3150/07-BEJ6110

Abstract

Let BH, K={BH, K(t), t∈ℝ+} be a bifractional Brownian motion in ℝd. We prove that BH, K is strongly locally non-deterministic. Applying this property and a stochastic integral representation of BH, K, we establish Chung’s law of the iterated logarithm for BH, K, as well as sharp Hölder conditions and tail probability estimates for the local times of BH, K.

We also consider the existence and regularity of the local times of the multiparameter bifractional Brownian motion B, ={B, (t), t∈ℝ+N} in ℝd using the Wiener–Itô chaos expansion.

Citation

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Ciprian A. Tudor. Yimin Xiao. "Sample path properties of bifractional Brownian motion." Bernoulli 13 (4) 1023 - 1052, November 2007. https://doi.org/10.3150/07-BEJ6110

Information

Published: November 2007
First available in Project Euclid: 9 November 2007

zbMATH: 1132.60034
MathSciNet: MR2364225
Digital Object Identifier: 10.3150/07-BEJ6110

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

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Vol.13 • No. 4 • November 2007
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