Windings of the stable Kolmogorov process

Abstract

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].

Cited by in corpus (3)

• Cramér's estimate for stable processes with power drift
• A stable Langevin model with diffusive-reflective boundary conditions
• Stable windings at the origin