Sample Path Properties of Bifractional Brownian Motion

Ciprian A. Tudor (1, 2) , Yimin Xiao (3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne
3 Department of Mathematics and Statistics

Let BH, K={BH, K(t), t \in R +} be a bifractional Brownian motion in R d. 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 BH̅, K̅={BH̅, K̅(t), t \in R +N} in R d using the Wiener–Itô chaos expansion.

Mots clés: 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

Domaines: Probabilités [math.PR]

Ciprian A. Tudor, Yimin Xiao. Sample Path Properties of Bifractional Brownian Motion. Bernoulli, 2007, 13 (4), pp.1023-1052. ⟨10.3150/07-BEJ6110⟩. ⟨hal-00083060v2⟩