The exit time of planar Brownian motion and the Phragmen-Lindelof principle

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:422

Article

Markowsky, Greg

关键词: Phragmen-Lindelof principle;    Brownian motion;    Analytic functions;    Exit times;   

DOI  :  10.1016/j.jmaa.2014.09.005

来源: Elsevier

【 摘 要 】

In this paper a version of the Phragmen-Lindelof principle is proved using probabilistic techniques. In particular, we will show that if the pth moment of the exit time of Brownian motion from a planar domain is finite, then an analytic function on that domain is either bounded by its supremum on the boundary or else goes to infinity along some sequence more rapidly than e(vertical bar z vertical bar 2P). We also provide a method of constructing domains whose exit time has finite pth moment. This allows us to give a general Phragmen-Lindelof principle for spiral-like and star-like domains, as well as a new proof of a theorem of Hansen. A number of auxiliary results are presented as well. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free