On the Wiener integral with respect to the fractional Brownian motion (Q700223)

Denote by \((B^H_t,0\leq t\leq T)\) the fractional Brownian motion of parameter \(H\in]0,1[\), by \({\mathcal H}_H\) its Gaussian space, and by \(K_H\) its reproducing kernel. The subspace of those integrands \(f\in {\mathcal H}_H\), for which \(\int^T_0 f(t)dB^H_t\) is well defined, and the adjoint of the closable operator \(K^{-1}_{1/2} \circ K_H\), are precisely determined. The cases \(H<1/2\) and \(H>1/2\) prove here once again to be different.