Windings of planar stable processes

2012/03/16 by Ron Doney, Ron A. Doney, Doney, Ron A. +2
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1203.3739

openalex publication_date 2012/03/16 · arxiv created 2012/12/22 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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