Stable windings at the origin

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Kyprianou, Andreas E.¹  Vakeroudis, Stavros M.² 

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Univ Aegean, Dept Math Track Stat & Actuarial Financial Math, Karlovassi 83200, Samos, Greece

关键词: Stable processes;    Winding numbers;    Self-similarity;    Lamperti transform;    Duality;    Time change;    Riesz-Bogdan-Zak transform;    Upcrossings;   

DOI  :  10.1016/j.spa.2018.02.004

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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