On the distribution of quadratic functionals of the ordinary and fractional Brownian motions

In this paper we discuss some distributional properties of quadratic functionals of the ordinary and fractional Brownian motions (fBms). As far as the ordinary Brownian motion (Bm) is concerned, those properties have been established extensively. A transition from the Bm to the fBm is not straightforward. Some difficulties associated with dealing with the fBm are explained, and a way to solving the problem is indicated, and some conjectures are given.