Probability Theory and Related Fields

, Volume 159, Issue 1–2, pp 237–272 | Cite as

Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion

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Abstract

The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter \(H=1/6\). We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.

Keywords

Fractional Brownian motion Cubic variation Convergence in law 

Mathematics Subject Classification

Primary 60G22; Secondary 60F17 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Krzysztof Burdzy
    • 1
  • David Nualart
    • 2
  • Jason Swanson
    • 3
  1. 1.University of WashingtonSeattleUSA
  2. 2.University of KansasLawrenceUSA
  3. 3.University of Central FloridaOrlandoUSA

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