Spectral characterization of the quadratic variation of mixed Brownian fractional Brownian motion

Details Spectral characterization of the quadratic variation of mixed Brownian fractional Brownian motion Spectral characterization of the quadratic variation of mixed Brownian fractional Brownian motion

2010-05-24

arxiv.org/abs/1005.4349v2

Mathematics

Probability

Scientific paper

Dzhaparidze and Spreij [5] showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. [2], where it is shown that the quadratic variation of the log-returns determines the hedging strategy.

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