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2013 | OriginalPaper | Chapter

Windings of Planar Stable Processes

Authors : R. A. Doney, S. Vakeroudis

Published in: Séminaire de Probabilités XLV

Publisher: Springer International Publishing

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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 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.

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previous chapter Langevin Process Reflected on a Partially Elastic Boundary II

next chapter An Elementary Proof that the First Hitting Time of an Open Set by a Jump Process is a Stopping Time

When we simply write: Brownian motion, we always mean real-valued Brownian motion, starting from 0. For two-dimensional Brownian motion, we indicate planar or complex BM.

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Title: Windings of Planar Stable Processes
Authors: R. A. Doney
S. Vakeroudis
Publisher: Springer International Publishing
Book: Séminaire de Probabilités XLV
Print ISBN: 978-3-319-00320-7

Electronic ISBN: 978-3-319-00321-4

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-319-00321-4_10