LEADER 02984nmm a2200469 i 4500 001 991003325449707536 006 m o d 007 cr ||| 008 170207t20142014sz a ob 001 0 eng d 020 $a9783319022314 (ebook) 035 $ab14316237-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a519.22$223 084 $aAMS 60H15 084 $aAMS 35R60 084 $aAMS 60H07 084 $aAMS 65-02 084 $aAMS 65C 084 $aLC QA3.L28 100 1 $aKruse, Raphael$0524888 245 10$aStrong and weak approximation of semilinear stochastic evolution equations$h[e-book] /$cRaphael Kruse 264 1$aCham [Switzerland] :$bSpringer,$c2014 300 $a1 online resource (xiv, 177 p. :$bil.) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x1617-9692 ;$v2093 500 $aBased on the author's thesis (doctoral)--Universität Bielefeld, 2012 504 $aIncludes bibliographical references (pages 171-174) and index 505 0 $aIntroduction ; 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 520 $aIn this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut's integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq 650 0$aEvolution equations 650 0$aStochastic integral equations 650 0$aStochastic partial differential equations 773 0 $aSpringereBooks 776 08$aPrinted edition:$z9783319022307 856 40$uhttp://link.springer.com/book/10.1007/978-3-319-02231-4$zAn electronic book accessible through the World Wide 907 $a.b14316237$b03-03-22$c07-02-17 912 $a991003325449707536 996 $aStrong and weak approximation of semilinear stochastic evolution equations$9821251 997 $aUNISALENTO 998 $ale013$b07-02-17$cm$d@ $e-$feng$gsz $h0$i0