Windings of the stable Kolmogorov process

Christophe Profeta (1) , Thomas Simon (2, 3)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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].

Mots clés: Integrated process; Harmonic measure; Hitting time; Stable Lévy process; Winding

Domaines: Probabilités [math.PR]

Christophe Profeta, Thomas Simon. Windings of the stable Kolmogorov process. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2015, XII, pp.115-127. ⟨hal-01018922⟩