000 03143nam a22005055i 4500
001 978-3-319-02231-4
003 DE-He213
005 20150803155057.0
007 cr nn 008mamaa
008 131114s2014 gw | s |||| 0|eng d
020 _a9783319022314
_9978-3-319-02231-4
024 7 _a10.1007/978-3-319-02231-4
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT021000
_2bisacsh
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aKruse, Raphael.
_eauthor.
245 1 0 _aStrong and Weak Approximation of Semilinear Stochastic Evolution Equations
_h[electronic resource] /
_cby Raphael Kruse.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXIV, 177 p. 4 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2093
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 -- Some Useful Variations of Gronwall’s Lemma -- Results on Semigroups and their Infinitesimal Generators -- A Generalized Version of Lebesgue’s Theorem -- References -- Index.
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 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aNumerical analysis.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aNumerical Analysis.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319022307
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2093
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02231-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c6947
_d6947