Sample path properties of bifractional Brownian motion

Tudor, Ciprian A.; Xiao, Yimin

Bernoulli, Tome 13 (2007) no. 1, p. 1023-1052 / Harvested from Project Euclid

Résumé

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.

Publié le : 2007-11-14
Classification: 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

@article{1194625601,
     author = {Tudor, Ciprian A. and Xiao, Yimin},
     title = {Sample path properties of bifractional Brownian motion},
     journal = {Bernoulli},
     volume = {13},
     number = {1},
     year = {2007},
     pages = { 1023-1052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1194625601}
}

Tudor, Ciprian A.; Xiao, Yimin. Sample path properties of bifractional Brownian motion. Bernoulli, Tome 13 (2007) no. 1, pp.  1023-1052. http://gdmltest.u-ga.fr/item/1194625601/