)>IJH=?J Some identities in law in terms of planar complex valued Ornstein-Uhlenbeck processes (Z t = X t + iY t , t ≥ 0) including planar Brownian motion are established and shown to be equivalent to the well known Bougerol identity for linear Brownian motion (β t , t ≥ 0): for any xed u > 0:with (β t , t ≥ 0) a Brownian motion, independent of β. These identities in law for 2-dimensional processes allow to study the distributions of hitting times T θ c ≡ inf{t :and more specically of

Using a generalization of the skew-product representation of planar Brownian motion and the analogue of Spitzer's 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 α ∈ (0, 2). We also study the case t → 0 and we prove some Laws of the Iterated Logarithm (LIL) for the (well-defined) winding process associated to our planar stable process. § When we simply write: Brownian motion, we always mean real-valued Brownian motion, starting from 0. For 2-dimensional Brownian motion, we indicate planar or complex BM.