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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

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Volume 10, Issue 3-4


Convergence rate for spherical processes with shifted centres*

N. Golyandina
  • Mathematical Department, St. Petersburg University Universitetsky av. 28, Petrodvorets, 198504, St. Petersburg, Russia. E-mail:
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Published Online: 2008-05-09 | DOI: https://doi.org/10.1515/mcma.2004.10.3-4.287

The paper is devoted to study of a modification of the random walks on spheres in a finite domain G ⊂ ℝm, m ≥ 2. It is proved that the considered spherical process with shifted centres converges to the boundary of G very rapidly. Namely, the average number of steps before fitting the ε-neighborhood of the boundary has the order of ln |ln ε| as ε → 0 instead of the standard order of |ln ε|. Thus, the spherical process with shifted centres can be effectively used for Monte Carlo solution of different problems of the mathematical physics related to the Laplace operator.

Keywords: random walk on spheres; spherical process with shifted centres; convergence rate; Laplace operator; Monte Carlo solution

About the article

Published Online: 2008-05-09

Published in Print: 2004-12-01

Citation Information: Monte Carlo Methods and Applications mcma, Volume 10, Issue 3-4, Pages 287–296, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2004.10.3-4.287.

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