Sample path properties of bifractional Brownian motion

Abstract

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

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