Strong and Weak Approximation of Semilinear Stochastic Evolution Equations by Raphael KruseStrong and Weak Approximation of Semilinear Stochastic Evolution Equations by Raphael Kruse

Strong and Weak Approximation of Semilinear Stochastic Evolution Equations

byRaphael Kruse

Paperback | November 25, 2013

Pricing and Purchase Info

$58.91 online 
$62.50 list price save 5%
Earn 295 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

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.

Title:Strong and Weak Approximation of Semilinear Stochastic Evolution EquationsFormat:PaperbackDimensions:177 pagesPublished:November 25, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:331902230X

ISBN - 13:9783319022307

Reviews

Table of Contents

Introduction.- Stochastic Evolution Equations in Hilbert Spaces.- Optimal Strong Error Estimates for Galerkin Finite Element Methods.- A Short Review of the Malliavin Calculus in Hilbert Spaces.- A Malliavin Calculus Approach to Weak Convergence.- Numerical Experiments.- Some Useful Variations of Gronwall's Lemma.- Results on Semigroups and their Infinitesimal Generators.- A Generalized Version of Lebesgue's Theorem.- References.- Index.