On squared fractional Brownian motions

We have proved recently that fractional Brownian motions with Hurst parameter H in (0, 1/2) satisfy a remarkable property: their squares are infinitely divisible. In the Brownian motion case (the case H = 1/2), this property is completely understood thanks to stochastic calculus arguments. We try here to take advantage of the stochastic calculus recently developed with respect to fractional Brownian motion, to construct analogous explanations of this property in the case H not equal 1/2.