02984nmm a2200469 i 4500991003325449707536m o d cr ||| 170207t20142014sz a ob 001 0 eng d9783319022314 (ebook)b14316237-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng519.2223AMS 60H15AMS 35R60AMS 60H07AMS 65-02AMS 65CLC QA3.L28Kruse, Raphael524888Strong and weak approximation of semilinear stochastic evolution equations[e-book] /Raphael KruseCham [Switzerland] :Springer,20141 online resource (xiv, 177 p. :il.)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,1617-9692 ;2093Based on the author's thesis (doctoral)--Universität Bielefeld, 2012Includes bibliographical references (pages 171-174) and indexIntroduction ; 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 experimentsIn 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 SEEqEvolution equationsStochastic integral equationsStochastic partial differential equationsSpringereBooksPrinted edition:9783319022307http://link.springer.com/book/10.1007/978-3-319-02231-4An electronic book accessible through the World Wide.b1431623703-03-2207-02-17991003325449707536Strong and weak approximation of semilinear stochastic evolution equations821251UNISALENTOle01307-02-17m@ -engsz 00