Hausdorff measures of the image, graph and level set of bifractional Brownian motion |
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Authors: | NaNa Luan |
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Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
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Abstract: | Let B H,K = {B H,K (t), t ∈ ?+} be a bifractional Brownian motion in ? d . This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of B H,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion. |
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