Skip to main content
SpringerLink
Log in

A Malliavin Calculus Approach to Weak Convergence

  • Chapter
  • First Online:
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2093))

  • 1833 Accesses

Abstract

The aim of this chapter is to present a new technique to analyze the weak error of convergence of spatially semidiscrete approximations and spatio-temporal discretizations of the solution of a linear stochastic evolution equation with additive noise.

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 29.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight 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. H.W. Alt, Lineare Funktionalanalysis, 5th revised edn. (Springer, Berlin, 2006)

    Google Scholar 

  2. C. Carstensen, An adaptive mesh-refining algorithm allowing for an H 1 stable L 2 projection onto Courant finite element spaces. Constr. Approx. 20(4), 549–564 (2004)

    Article  MathSciNet  MATH  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. A. Debussche, Weak approximation of stochastic partial differential equations: The nonlinear case. Math. Comput. 80(273), 89–117 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Debussche, J. Printems, Weak order for the discretization of the stochastic heat equation. Math. Comput. 78(266), 845–863 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Kovács, S. Larsson, F. Lindgren, Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise. BIT Numer. Math. 52(1), 85–108 (2012)

    Article  MATH  Google Scholar 

  7. M. Kovács, S. Larsson, F. Lindgren, Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes. BIT Numer. Math. 53(2), 497–525 (2012). Preprint [arXiv:1203.2029v1]

    Google Scholar 

  8. C. Prévôt, M. Röckner, A Concise Course on Stochastic Partial Differential Equations. Lecture Notes in Mathematics, vol. 1905 (Springer, Berlin, 2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bielefeld University, Bielefeld, Germany

    Raphael Kruse

Authors
  1. Raphael Kruse
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kruse, R. (2014). A Malliavin Calculus Approach to Weak Convergence. In: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations. Lecture Notes in Mathematics, vol 2093. Springer, Cham. https://doi.org/10.1007/978-3-319-02231-4_5

Download citation

Publish with us

Policies and ethics

Search

Navigation