Bernoulli

  • Bernoulli
  • Volume 13, Number 4 (2007), 1023-1052.

Sample path properties of bifractional Brownian motion

Ciprian A. Tudor and Yimin Xiao

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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.

Article information

Source
Bernoulli, Volume 13, Number 4 (2007), 1023-1052.

Dates
First available in Project Euclid: 9 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1194625601

Digital Object Identifier
doi:10.3150/07-BEJ6110

Mathematical Reviews number (MathSciNet)
MR2364225

Zentralblatt MATH identifier
1132.60034

Keywords
bifractional Brownian motion chaos expansion Chung’s law of the iterated logarithm Hausdorff dimension level set local times multiple Wiener–Itô stochastic integrals self-similar Gaussian processes small ball probability

Citation

Tudor, Ciprian A.; Xiao, Yimin. Sample path properties of bifractional Brownian motion. Bernoulli 13 (2007), no. 4, 1023--1052. doi:10.3150/07-BEJ6110. https://projecteuclid.org/euclid.bj/1194625601


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