I would like to know more about this way of representing the fBm process.
Define: $$K_H(t,u) = (t-u)^\kappa_+ - (-u)^\kappa_+,$$ where $\kappa = H - 1/2$. The Mandelbrot Van Ness representation of the fBm process in terms of integral \begin{equation}\label{eq:mvn} B_t^H = \left( \int_{\mathbb{R}^+} ((1+s)^\kappa - s^\kappa)^2 ds + \frac{1}{2H} \right)^{1/2} \int_{\mathbb{R}} K_{H}(t,u)dW_u \end{equation}
I don't understand where the parts comes from, and if there are some papers concerning this representation that anyone could share with me.
$B_{t}^{H}=c_{1}(H) \int_{\mathbb{R}_{-}}(-r)^{H-1 / 2}\left[d W_{t+r}-d W_{r}\right]=c_{1}(H)\left\{\int_{-\infty}^{0}\left[(t-r)^{H-1 / 2}-(-r)^{H-1 / 2}\right] d W_{r}-\int_{0}^{t}(t-r)^{H-1 / 2} d W_{r}\right\}$
with $c_{1}(H)=\frac{[2 H \sin (\pi H) \Gamma(2 H)]^{\frac{1}{2}}}{\Gamma(H+1 / 2)}$.