The size of an analytic function as measured by Lévy's time change
type: Item
instance of: scholarly article
title: The size of an analytic function as measured by Lévy's time change
zbMATH Open document ID: 0574.60087
author: Terry R. McConnell
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: The author proves that for a wide class of functions \(\Phi\), f analytic in the unit disk and \(| f'(0)| \geq 1\), it is true that \(E\Phi\) (\(\nu\) (f))\(\geq E(\Phi (\nu (z))\) where \(\nu (f)=\int^{\tau}_{0}| f'(B(s))|^ 2ds\), \(\tau\) being the exit time of the standard, plane, Brownian motion from the unit disk. Also the conjecture P(\(\lambda\leq \nu (f))\geq P(\lambda \leq \nu (z))\) is proved impossible in general.
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 3917408
zbMATH Keywords: complex Brownian motion
zbMATH Keywords: analytic functions
zbMATH Keywords: Brownian motion
reviewed by: Henryk Gzyl
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992921
OpenAlex ID: W1964829980
DOI: 10.1214/AOP/1176992921
description: scientific article; zbMATH DE number 3917408