Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion
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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.
KeywordsFractional Brownian motion Cubic variation Convergence in law
Mathematics Subject ClassificationPrimary 60G22; Secondary 60F17
The authors are grateful for the careful reading and helpful suggestions of an anonymous referee. Krzysztof Burdzy was partially supported by Grant DMS-1206276 from the NSF and by Grant N N201 397137 from the MNiSW, Poland. David Nualart was partially supported by Grant DMS-1208625 from the NSF.
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