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On convex hull of d-dimensional fractional Brownian motion

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  • Davydov, Yu.

Abstract

It is well known that for standard Brownian motion {B(t),t≥0} with values in Rd its convex hull V(t)=conv{B(s),s≤t} with probability 1 contains 0 as an interior point for each t>0 (see Evans, 1985). The aim of this note is to state the analogous property for d-dimensional fractional Brownian motion.

Suggested Citation

  • Davydov, Yu., 2012. "On convex hull of d-dimensional fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 37-39.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:37-39
    DOI: 10.1016/j.spl.2011.09.004
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    References listed on IDEAS

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    1. Lavancier, Frédéric & Philippe, Anne & Surgailis, Donatas, 2009. "Covariance function of vector self-similar processes," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2415-2421, December.
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    Cited by:

    1. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.

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