Strong and weak approximation of semilinear stochastic evolution equations [electronic resource] / Raphael Kruse.
Kruse, Raphael, author.
2014
QA3 .L28 no. 2093
Available Online

Linked e-resources

Linked Resource
Online Access

Details

Title
Strong and weak approximation of semilinear stochastic evolution equations [electronic resource] / Raphael Kruse.
Author
Kruse, Raphael, author.
ISBN
9783319022314 electronic book
3319022318 electronic book
9783319022307
331902230X
Published
Cham [Switzerland] : Springer, [2014]
Copyright
©2014
Language
English
Description
1 online resource (xiv, 177 pages) : illustrations.
Call Number
QA3 .L28 no. 2093
Dewey Decimal Classification
519.2/2
Summary
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.
Note
Based on the author's thesis (doctoral)--Universität Bielefeld, 2012.
Bibliography, etc. Note
Includes bibliographical references (pages 171-174) and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from PDF title page (SpringerLink, viewed Jan. 2, 2014).
Series
Lecture notes in mathematics (Springer-Verlag) ; 2093. 0075-8434
Available in Other Form
Original 331902230X
Linked Resources
Online Access
Record Appears in
Online Resources > Ebooks
All Resources
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.

Browse Subjects

Show more subjects...

Statistics

from
to
Export