2014/07/07 by Christophe Profeta, Profeta, Christophe, Thomas Simon +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1407.1597
arxiv created 2014/07/07 · openalex publication_date 2014/07/07 · arxiv updated 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We investigate the windings around the origin of the two-dimensional Markov process (X,L) having the stable Lévy process L and its primitive X as coordinates, in the non-trivial case when |L| is not a subordinator. First, we show that these windings have an almost sure limit velocity, extending McKean's result [McK63] in the Brownian case. Second, we evaluate precisely the upper tails of the distribution of the half-winding times, connecting the results of our recent papers [CP14, PS14].