Windings of planar stable processes
| Autor: | Doney, Ron A., Vakeroudis, Stavros |
|---|---|
| Přispěvatelé: | Department of Mathematics [Manchester] (School of Mathematics), University of Manchester [Manchester], Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
exit time from a cone
Probability (math.PR) windings [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Mathematics::Probability Lévy processes Spitzer's Theorem FOS: Mathematics Stable processes skew-product representation Lamperti's relation Brownian motion AMS: Primary: 60G52 60G51 60F05 60J65 secondary: 60E07 60B12 60G18 Mathematics - Probability Law of the Iterated Logarithm (LIL) for small times |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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