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Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion
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math.PR
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brownianmotionsubsequencesconvergencecubicfractionalsignedvariation
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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.
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