The paper is devoted to study of a modification of the random walks on spheres in a finite domain *G* ⊂ ℝ^{m}, *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.

# Monte Carlo Methods and Applications

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# Convergence rate for spherical processes with shifted centres^{*}

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Get Access to Full TextKeywords: 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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