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 0005202oam 2200589 450 99646598650331620210521142707.03-540-47884-110.1007/3-540-47884-1(CKB)1000000000211731(SSID)ssj0000318345(PQKBManifestationID)11265157(PQKBTitleCode)TC0000318345(PQKBWorkID)10310389(PQKB)10559312(DE-He213)978-3-540-47884-3(MiAaPQ)EBC3062450(MiAaPQ)EBC6414012(PPN)123720400(EXLCZ)99100000000021173120210521d2002 uy 0engurnn|008mamaatxtccrIntegrated formal methods Third International Conference, IFM 2002, Turku, Finland, May 15-18, 2002 : proceedings /Michael Butler, Luigia Petre, Kaisa Sere, eds1st ed. 2002.Berlin, Germany ;New York, New York :Springer,[2002]©20021 online resource (X, 401 p.) Lecture Notes in Computer Science,0302-9743 ;2335Bibliographic Level Mode of Issuance: Monograph3-540-43703-7 Includes bibliographical references and index.Invited Talk: Eran Gery -- Rhapsody: A Complete Life-Cycle Model-Based Development System -- Integration, Simulation, Animation -- An Integrated Semantics for UML Class, Object and State Diagrams Based on Graph Transformation -- Stochastic Process Algebras Meet Eden -- From Specifcation to Verifcation -- From Implicit Specifications to Explicit Designs in Reactive System Development -- Basic-REAL: Integrated Approach for Design, Specification and Verification of Distributed Systems -- Assume-Guarantee Algorithms for Automatic Detection of Software Failures -- Statecharts and B: Integration and Translation -- Contributions for Modelling UML State-Charts in B -- Translating Statecharts to B -- Invited Talk: Shmuel Katz -- A Framework for Translating Models and Specifications -- Model Checkers and Theorem Provers -- Model Checking Object-Z Using ASM -- Formalization of Cadence SPW Fixed-Point Arithmetic in HOL -- Formally Linking MDG and HOL Based on a Verified MDG System -- Links between Object-Z and CSP -- Refinement in Object-Z and CSP -- Combining Specification Techniques for Processes, Data and Time -- An Integration of Real-Time Object-Z and CSP for Specifying Concurrent Real-Time Systems -- Invited Talk: Stuart Kent -- Model Driven Engineering -- Combining Graphical and Formal Approaches -- The Design of a Tool-Supported Graphical Notation for Timed CSP -- Combining Graphical and Formal Development of Open Distributed Systems -- Translations between Textual Transition Systems and Petri Nets -- Refinement and Proof -- Specification and Proof of Liveness Properties under Fairness Assumptions in B Event Systems -- Minimally and Maximally Abstract Retrenchments.The third in a series of international conferences on Integrated Formal Methods, IFM 2002, was held in Turku, Finland, May 15–17, 2002. Turku, situated in the south western corner of the country, is the former capital of Finland. The ? conference was organized jointly by Abo Akademi University and Turku Centre for Computer Science. The theme of IFM 1999 was the integration of state and behavioral based formalisms. For IFM 2000 this was widened to include all aspects pertaining to the integration of formal methods and formal notations. One of the goals of IFM 2002 was to further investigate these themes. Moreover, IFM 2002 explored the relations between formal methods and graphical notations, especially the industrialstandardlanguageforsoftwaredesign,theUni?edModelingLanguage (UML). The themes of IFM 2002 re?ect what we believe is a growing trend in the Formal Methods and Software Engineering research communities. Over the last threedecades,computerscientistshavedevelopedarangeofformalismsfocusing on particular aspects of behavior or analysis, such as sequential program str- tures,concurrentprogramstructures,dataandinformationstructures,temporal reasoning, deductive proof, and model checking. Much e?ort is now being - voted to integrating these methods in order to combine their advantages and ensure they scale up to industrial needs. Graphical notations are now widely used in software engineering and there is growing recognition of the importance ofprovidingthesewiththeformalunderpinningsandformalanalysiscapabilities found in formal methods.Lecture Notes in Computer Science,0302-9743 ;2335Formal methods (Computer science)CongressesFormal methods (Computer science)004/.01/51Sere K(Kaisa),1954-Petre Luigia1974-Butler Michael1967-International Conference on Integrated Formal MethodsMiAaPQMiAaPQUtOrBLWBOOK996465986503316Integrated Formal Methods2860239UNISA