Strong and weak approximation of semilinear stochastic evolution equations / Raphael Kruse
Type de document : MonographieCollection : Lecture notes in mathematics, 2093Langue : anglais.Pays: Swisse.Éditeur : Cham : Springer, cop. 2014Description : 1 vol. (XIV-177 p.) : fig. ; 24 cmISBN: 9783319022307.ISSN: 0075-8434.Bibliographie : Bibliogr. p. 171-174. Index.Sujet MSC : 60-02, Research exposition (monographs, survey articles) pertaining to probability theory60H15, Probability theory and stochastic processes - Stochastic analysis, Stochastic partial differential equations
35R60, Miscellaneous topics in partial differential equations, PDEs with randomness, stochastic partial differential equations
60H07, Probability theory and stochastic processes - Stochastic analysis, Stochastic calculus of variations and the Malliavin calculusNote de thèse: Texte remanié de : , Thèse de doctorat, mathématiques, 2012, Bielefeld UniversityEn-ligne : Sommaire | Zentralblatt | MathSciNet
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Monographie
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CMI Salle 1 | 60 KRU (Browse shelf(Opens below)) | Available | 12278-01 |
Bibliogr. p. 171-174. Index
Texte remanié de : Thèse de doctorat mathématiques 2012 Bielefeld University
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. (Source : Springer)
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