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arXiv · 1306.1998

Large Deviations of Shepp Statistics for Fractional Brownian Motion

Enkelejd Hashorva·Zhongquan Tan
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Abstract

Define the incremental fractional Brownian field $B_{H}(s+τ)-B_{H}(s), H\in (0,1)$, where $B_{H}(s)$ is a standard fractional Brownian motion with Hurst index $H\in(0,1)$. In this paper we derive the exact asymptotic behaviour of the maximum $\max_{(τ,s)\in[0,1]\times[0,T]} (B_{H}(s+τ)-B_{H}(s)) $ for any $H\in (0,1/2)$ complimenting thus the result of Zholud (2008) for the Brownian motion.

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BibTeXRIS

Enkelejd Hashorva, Zhongquan Tan. 2013-06-09. Large Deviations of Shepp Statistics for Fractional Brownian Motion. https://doi.org/10.1016/j.spl.2013.06.013

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