Sample Path Properties of Bifractional Brownian Motion

Abstract

Let $B^{H,K}=\{B^{H,K}(t),t\in {\mathbb{R}}_{+}\}$ be a bifractional Brownian motion in ${\mathbb{R}}^d$. We prove that $B^{H,K}$ is strongly locally nondeterministic. 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 the regularity of the local times of multiparameter bifractional Brownian motion $B^{\bar{H},\bar{K}}=\{B^{\bar{H},\bar{K}}(t),t\in {\mathbb{R}}_{+}^N\}$ in ${\mathbb{R}}^d$ using Wiener-Itô chaos expansion.