Windings of planar stable processes

Using a generalization of the skew-product representation of planar Brownian motion and the analogue of Spitzers celebrated asymptotic Theorem for stable processes due to Bertoin and Werner, for which we provide a new easy proof, we obtain some limit Theorems for the exit time from a cone of stable processes of index $alphain(0,2)$. We also study the case $trightarrow0$ and we prove some Laws of the Iterated Logarithm (LIL) for the (well-defined) winding process associated to our planar stable process.