Level crossings of a Cauchy process
type: Item
instance of: scholarly article
title: Level crossings of a Cauchy process
zbMATH Open document ID: 0602.60059
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: The authors use the well-known skew-product representation of planar Brownian motion, and a simple argument involving Brownian scaling and renewal theory for an embedded random walk, to establish the asymptotic behaviour of numbers of large, small, and medium crossings of zero by a Cauchy process. They further apply the results of a comparison paper to establish results for different kinds of crossings at two different levels.
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 3971910
zbMATH Keywords: skew-product representation of planar Brownian motion
zbMATH Keywords: Brownian scaling and renewal theory
zbMATH Keywords: crossings of zero by a Cauchy process
author: Jim Pitman
author: Marc Yor
reviewed by: Wilfrid S. Kendall
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992437
OpenAlex ID: W2037783389
DOI: 10.1214/AOP/1176992437
description: scientific article; zbMATH DE number 3971910