Skip to main content
SpringerLink
Log in

Combining Space-Time Multigrid Techniques with Multilevel Monte Carlo Methods for SDEs

  • Conference paper
  • First Online:
Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

Included in the following conference series:

Abstract

In this work we combine multilevel Monte Carlo methods for time-dependent stochastic differential equations with a space-time multigrid method. The idea is to use the space-time hierarchy from the multilevel Monte Carlo method also for the solution process of the arising linear systems. This symbiosis leads to a robust and parallel method with respect to space, time and probability. We show the performance of this approach by several numerical experiments which demonstrate the advantages of this approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Andersson, R. Kruse, S. Larsson, Duality in refined Sobolev-Malliavin spaces and weak approximation of SPDE. Stoch. Partial Differ. Equ. Anal. Comput. 4, 113–149 (2016)

    MathSciNet  MATH  Google Scholar 

  2. A. Barth, A. Lang, Simulation of stochastic partial differential equations using finite element methods. Stochastics 84(2–3), 217–231 (2012)

    Article  MathSciNet  Google Scholar 

  3. G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Its Applications, vol. 44 (Cambridge University Press, Cambridge, 1992)

    Google Scholar 

  4. M. Gander, M. Neumüller, Analysis of a new space-time parallel multigrid algorithm for parabolic problems. SIAM J. Sci. Comput. 38(4), A2173–A2208 (2016)

    Article  MathSciNet  Google Scholar 

  5. M.B. Giles, Multilevel Monte Carlo path simulation. Oper. Res. 56, 607–617 (2008)

    Article  MathSciNet  Google Scholar 

  6. A. Lang, A note on the importance of weak convergence rates for SPDE approximations in multilevel Monte Carlo schemes, in Monte Carlo and Quasi-Monte Carlo Methods, MCQMC, Leuven, ed. by R. Cools, D. Nuyens (Springer, Cham, 2016), pp. 489–505

    Google Scholar 

  7. G.J. Lord, C.E. Powell, T. Shardlow, An Introduction to Computational Stochastic PDEs Cambridge. Texts in Applied Mathematics (Cambridge University Press, New York, 2014)

    Google Scholar 

  8. G.N. Milstein, M.V. Tretyakov, Stochastic Numerics for Mathematical Physics. Scientific Computation (Springer, Berlin, 2004)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Johannes Kepler University, Institute of Computational Mathematics, Linz, Austria

    Martin Neumüller

  2. Johannes Kepler University, Doctoral Program “Computational Mathematics” and Institute for Stochastics, Linz, Austria

    Andreas Thalhammer

Authors
  1. Martin Neumüller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Thalhammer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Martin Neumüller or Andreas Thalhammer .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Neumüller, M., Thalhammer, A. (2018). Combining Space-Time Multigrid Techniques with Multilevel Monte Carlo Methods for SDEs. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_47

Download citation

Publish with us

Policies and ethics

Search

Navigation