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].
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [12 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01018922
Contributor : Christophe Profeta <>
Submitted on : Sunday, July 6, 2014 - 9:05:42 PM
Last modification on : Tuesday, July 3, 2018 - 11:47:06 AM
Long-term archiving on : Monday, October 6, 2014 - 10:40:09 AM

Files

Windings2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01018922, version 1
  • ARXIV : 1407.1597

Collections

Citation

Christophe Profeta, Thomas Simon. Windings of the stable Kolmogorov process. 2014. ⟨hal-01018922⟩

Share

Metrics

Record views

455

Files downloads

118