Distributions of quadratic functionals of the fractional Brownian motion based on a martingale approximation

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I discuss some computational problems associated with distributions of statistics arising from the fractional Brownian motion (fBm). In particular, I deal with (ratios of) its quadratic functionals. While it is easy in principle to deal with the standard Bm, the fBm is difficult to analyse because of its non-semimartingale nature. Here I suggest how to derive and compute the distributions of such functionals by using a martingale approximation.