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Hausdorff measures of the image, graph and level set of bifractional Brownian motion

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Abstract

Let B H,K = {B H,K(t), t ∈ ℝ+} be a bifractional Brownian motion in ℝd. 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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  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    NaNa Luan

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  1. NaNa Luan
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Correspondence to NaNa Luan.

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Luan, N. Hausdorff measures of the image, graph and level set of bifractional Brownian motion. Sci. China Math. 53, 2973–2992 (2010). https://doi.org/10.1007/s11425-010-4100-x

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  • DOI: https://doi.org/10.1007/s11425-010-4100-x

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