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Sample path properties of bifractional Brownian motion. (English) Zbl 1132.60034

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 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 \(B^{\overline H,\overline K}=\{B^{\overline H,\overline K}(t)\), \(t \in \mathbb R_+^N\}\) in \(\mathbb R^d\) using the Wiener-Itô chaos expansion.

MSC:

60G17 Sample path properties
60G15 Gaussian processes
60J55 Local time and additive functionals
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