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Deterministic Particle Methods for High Dimensional Fokker-Planck Equations

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2007

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Venkiteswaran, G.

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http://nbn-resolving.de/urn:nbn:de:bsz:352-254011
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https://doi.org/10.1007/978-3-540-46222-4_10
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GRIEBEL, Michael, ed., Marc A. SCHWEITZER, ed.. Meshfree Methods for Partial Differential Equations III. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, pp. 165-183. Lecture Notes in Computational Science and Engineering. ISBN 978-3-540-46214-9. Available under: doi: 10.1007/978-3-540-46222-4_10

Zusammenfassung

We consider a mathematical model for polymeric liquids which requires the solution of high-dimensional Fokker-Planck equations related to stochastic differential equations. While Monte-Carlo (MC) methods are classically used to construct approximate solutions in this context, we consider an approach based on Quasi- Monte-Carlo (QMC) approximations. Although QMC has proved to be superior to MC in certain integration problems, the advantages are not as pronounced when dealing with stochastic differential equations. In this article, we illustrate the basic difficulty which is related to the construction of QMC product measures.

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510 Mathematik

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ISO 690JUNK, Michael, G. VENKITESWARAN, 2007. Deterministic Particle Methods for High Dimensional Fokker-Planck Equations. In: GRIEBEL, Michael, ed., Marc A. SCHWEITZER, ed.. Meshfree Methods for Partial Differential Equations III. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, pp. 165-183. Lecture Notes in Computational Science and Engineering. ISBN 978-3-540-46214-9. Available under: doi: 10.1007/978-3-540-46222-4_10
BibTex
@incollection{Junk2007Deter-25401,
  year={2007},
  doi={10.1007/978-3-540-46222-4_10},
  title={Deterministic Particle Methods for High Dimensional Fokker-Planck Equations},
  isbn={978-3-540-46214-9},
  publisher={Springer Berlin Heidelberg},
  address={Berlin, Heidelberg},
  series={Lecture Notes in Computational Science and Engineering},
  booktitle={Meshfree Methods for Partial Differential Equations III},
  pages={165--183},
  editor={Griebel, Michael and Schweitzer, Marc A.},
  author={Junk, Michael and Venkiteswaran, G.}
}
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