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