Windings of planar stable processes

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00679710
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Submitted on : Saturday, December 22, 2012 - 1:02:36 PM
Last modification on : Sunday, March 31, 2019 - 1:21:58 AM
Long-term archiving on: Saturday, March 23, 2013 - 3:46:50 AM

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  • HAL Id : hal-00679710, version 3
  • ARXIV : 1203.3739

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Ron A. Doney, Stavros Vakeroudis. Windings of planar stable processes. 2012. ⟨hal-00679710v3⟩

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