Windings of planar stable processes

Details Windings of planar stable processes Windings of planar stable processes

2012-03-16

arxiv.org/abs/1203.3739v1

Mathematics

Probability

Scientific paper

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 $\alpha\in(0,2)$. We also study the case $t\rightarrow0$ and we prove some Laws of the Iterated Logarithm (LIL) for the (well-defined) winding process associated to our planar stable process.

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