Skip to main content
  • Book
  • © 2014

Strong and Weak Approximation of Semilinear Stochastic Evolution Equations

Authors:

  • Employing Galerkin finite element methods closes the gap between theoretical convergence results and standard PDE solvers in widely used software packages

  • Derives the optimal order of strong convergence through optimal regularity results

  • Includes a self-contained introduction to Malliavin calculus

  • Effectively approaches weak convergence for SPDEs with stochastic coefficients by avoiding Kolmogorov’s backward equation

  • Includes supplementary material: sn.pub/extras

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

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 37.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
  2. Introduction

    • Raphael Kruse
    Pages 1-10
  3. Numerical Experiments

    • Raphael Kruse
    Pages 129-153
  4. Back Matter

    Pages 155-180

About this book

In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book.

The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.

Keywords

  • 65C30,60H15,65M60,60H07,35B65
  • Galerkin finite element methods
  • Malliavin Calculus
  • SPDE
  • Spatio-temporal regularity
  • Strong and weak convergence
  • partial differential equations

Authors and Affiliations

  • Dept. of Mathematics, Bielefeld University, Bielefeld, Germany

    Raphael Kruse

Bibliographic Information

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 37.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions