• 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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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.

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

First available in Project Euclid: 9 November 2007

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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


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

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