Sample Path Properties of Bifractional Brownian Motion
Résumé
Let $B^{H, K}= \big\{B^{H, K}(t),\, t \in \R_+ \big\}$ be a bifractional Brownian motion in $\R^d$. 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 $B^{\overline{H}, \overline{K}}= \big\{B^{\overline{H}, \overline{K}}(t),\, t \in \R^N_+ \big\}$ in $\R^d$ using Wiener-Itô chaos expansion.