Strong and Weak Approximation of Semilinear Stochastic Evolution Equations (Lecture Notes in Mathematics, 2093) - Softcover

Kruse, Raphael

 
9783319022307: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations (Lecture Notes in Mathematics, 2093)
Softcover
ISBN 10: 331902230X ISBN 13: 9783319022307
Publisher: 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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2013
Language
English
ISBN 10 
331902230X
ISBN 13 
9783319022307
Binding
Paperback
Number of pages
191