Some sample path properties of multifractional Brownian motion

Paul Balança

Stochastic Processes and their Applications, 2015, vol. 125, issue 10, 3823-3850

Abstract: The geometry of the multifractional Brownian motion (mBm) is known to present a complex and surprising form when the Hurst function is greatly irregular. Nevertheless, most of the literature devoted to the subject considers sufficiently smooth cases which lead to sample paths locally similar to a fractional Brownian motion (fBm). The main goal of this paper is therefore to extend these results to a more general frame and consider any type of continuous Hurst function. More specifically, we mainly focus on obtaining a complete characterisation of the pointwise Hölder regularity of the sample paths, and the Box and Hausdorff dimensions of the graph. These results, which are somehow unusual for a Gaussian process, are illustrated by several examples, presenting in this way different aspects of the geometry of the mBm with irregular Hurst functions.

Keywords: 2-microlocal analysis; Box dimension; Hausdorff dimension; Hölder regularity; Multifractional Brownian motion (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:10:p:3823-3850

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DOI: 10.1016/j.spa.2015.05.008

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