Stable windings at the origin

Andreas E. Kyprianou, Stavros Vakeroudis

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
30 Downloads (Pure)

Abstract

In 1996, Bertoin and Werner demonstrated a functional limit theorem, characterising the windings of planar isotropic stable processes around the origin for large times, thereby complementing known results for planar Brownian motion. The question of windings at small times can be handled using scaling. Nonetheless we examine the case of windings at the origin using new techniques from the theory of self-similar Markov processes. This allows us to understand upcrossings of (not necessarily symmetric) stable processes over the origin for large and small times in the one-dimensional setting.
Original languageEnglish
Pages (from-to)4309-4325
Number of pages17
JournalStochastic Processes and their Applications
Volume128
Issue number12
Early online date19 Feb 2018
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Duality
  • Lamperti transform
  • Riesz–Bogdan–Żak transform
  • Self-similarity
  • Stable processes
  • Time change
  • Upcrossings
  • Winding numbers

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Stable windings at the origin'. Together they form a unique fingerprint.

Cite this