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Asymptotic behavior of local times related statistics for fractional Brownian motion
Mark Podolskij, Mathieu Rosenbaum · 2017-10-23 · via math.PR updates on arXiv.org

We consider high frequency observations from a fractional Brownian motion. Inspired by the work of Jean Jacod in a diffusion setting, we investigate the asymptotic behavior of various classical statistics related to the local times of the process. We show that as in the diffusion case, these statistics indeed converge to some local times up to a constant factor. As a corollary, we provide limit theorems for the quadratic variation of the absolute value of a fractional Brownian motion.

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