Geometric and Functional Analysis

, Volume 22, Issue 3, pp 558–587 | Cite as

The rate of convergence of the Walk on Spheres Algorithm

  • Ilia Binder
  • Mark Braverman


In this paper we examine the rate of convergence of one of the standard algorithms for emulating exit probabilities of Brownian motion, the Walk on Spheres (WoS) algorithm. We obtain a complete characterization of the rate of convergence of WoS in terms of the local geometry of a domain.

Keywords and phrases

Walk on spheres algorithm harmonic measure potential theory 

Mathematics Subject Classification (2000)

60G42 65C05 31B25 31B05 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Department of Computer SciencePrinceton UniversityPrincetonUSA

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