Asymptotic laws of planar Brownian motion
type: Item
instance of: scholarly article
title: Asymptotic laws of planar Brownian motion
zbMATH Open document ID: 0607.60070
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: This paper presents a unified approach to various asymptotic results for planar Brownian motion, involving such objects as additive functionals or windings about points of the plane. In particular, the authors obtain the joint asymptotic law of the windings about several points of the plane, thus extending a result due to \textit{F. Spitzer} [Trans. Am. Math. Soc. 87, 187-197 (1958; Zbl 0089.136)] in the case of a single point. The main tools are stochastic calculus, especially Knight's theorem on orthogonal continuous martingales, and excursion theory. A very important role is also played by the representation of planar Brownian motion in polar coordinates (the so-called skew-product representation), which is used simultaneously with several different origins.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 3982212
zbMATH Keywords: planar Brownian motion
zbMATH Keywords: additive functionals
zbMATH Keywords: windings about points of the plane
zbMATH Keywords: Knight's theorem
author: Jim Pitman
author: Marc Yor
reviewed by: J.-F. Le Gall
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992436
OpenAlex ID: W2044314485
DOI: 10.1214/AOP/1176992436
description: scientific article; zbMATH DE number 3982212