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arXiv · 1210.1560

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

Krzysztof Burdzy·David Nualart·Jason Swanson
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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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Krzysztof Burdzy, David Nualart, Jason Swanson. 2012-10-04. Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion. https://arxiv.org/abs/1210.1560

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