LEADER 03800nam 22006375 450 001 996198773803316 005 20200630042313.0 010 $a3-319-02231-8 024 7 $a10.1007/978-3-319-02231-4 035 $a(CKB)3710000000078594 035 $a(DE-He213)978-3-319-02231-4 035 $a(SSID)ssj0001067983 035 $a(PQKBManifestationID)11600988 035 $a(PQKBTitleCode)TC0001067983 035 $a(PQKBWorkID)11094389 035 $a(PQKB)10346204 035 $a(MiAaPQ)EBC3107013 035 $a(PPN)176105727 035 $a(EXLCZ)993710000000078594 100 $a20131114d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStrong and Weak Approximation of Semilinear Stochastic Evolution Equations$b[electronic resource] /$fby Raphael Kruse 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XIV, 177 p. 4 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2093 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-02230-X 327 $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 -- Some Useful Variations of Gronwall?s Lemma -- Results on Semigroups and their Infinitesimal Generators -- A Generalized Version of Lebesgue?s Theorem -- References -- Index. 330 $aIn this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut?s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2093 606 $aNumerical analysis 606 $aProbabilities 606 $aPartial differential equations 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aNumerical analysis. 615 0$aProbabilities. 615 0$aPartial differential equations. 615 14$aNumerical Analysis. 615 24$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 676 $a519.22 700 $aKruse$b Raphael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0524888 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996198773803316 996 $aStrong and weak approximation of semilinear stochastic evolution equations$9821251 997 $aUNISA