Strong and Weak Approximation of Semilinear Stochastic Evolution Equations - Couverture souple

Kruse, Raphael

 
9783319022307: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
Couverture souple
ISBN 10 : 331902230X ISBN 13 : 9783319022307
Editeur : Springer, 2013

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2013
Langue
anglais
ISBN 10 
331902230X
ISBN 13 
9783319022307
Reliure
Broché
Nombre de pages
196
Coordonnées du fabricant
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

Europaplatz 3
Heidelberg
69115
Allemagne