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URN: urn:nbn:de:0030-drops-1393
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Monte Carlo solution for the Poisson equation on the base of spherical processes with shifted centres

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Abstract

We consider a class of spherical processes rapidly
converging to the boundary (so called Decentred
Random Walks on Spheres or spherical processes
with shifted centres) in comparison with the
standard walk on spheres. The aim is to compare
costs of the corresponding Monte Carlo estimates
for the Poisson equation. Generally, these costs
depend on the cost of simulation of one trajectory
and on the variance of the estimate.
It can be proved that for the Laplace equation the
limit variance of the estimation doesn't depend on
the kind of spherical processes. Thus we have very
effective estimator based on the decentred random
walk on spheres. As for the Poisson equation, it
can be shown that the variance is bounded by a
constant independent of the kind of spherical
processes (in standard form or with shifted
centres). We use simulation for a simple model
example to investigate variance behavior in more
details.

BibTeX - Entry

@InProceedings{golyandina:DagSemProc.04401.7,
  author =	{Golyandina, Nina},
  title =	{{Monte Carlo solution for the Poisson equation on the base of spherical processes with shifted centres}},
  booktitle =	{Algorithms and Complexity for Continuous Problems},
  pages =	{1--8},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4401},
  editor =	{Thomas M\"{u}ller-Gronbach and Erich Novak and Knut Petras and Joseph F. Traub},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/139},
  URN =		{urn:nbn:de:0030-drops-1393},
  doi =		{10.4230/DagSemProc.04401.7},
  annote =	{Keywords: Poisson equation , Laplace operator , Monte Carlo solution , spherical process , random walk on spheres , rate of convergence}
}

Keywords: Poisson equation , Laplace operator , Monte Carlo solution , spherical process , random walk on spheres , rate of convergence
Seminar: 04401 - Algorithms and Complexity for Continuous Problems
Issue date: 2005
Date of publication: 19.04.2005


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