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

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)


In this paper a version of the Phragmén–Lindelöf principle is proved using probabilistic techniques. In particular, we will show that if the p th 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 ∞ along some sequence more rapidly than e|z|2p. We also provide a method of constructing domains whose exit time has finite pth moment. This allows us to give a general Phragmén–Lindelöf 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.
Original languageEnglish
Pages (from-to)638-645
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2015


  • Phragmen–Lindelof principle
  • Brownian motion
  • Analytic functions
  • Exit times

Cite this