Strong and Weak Approximation of Semilinear Stochastic Evolution Equations (Lecture Notes in Mathematics, Band 2093) - Softcover

Kruse, Raphael

Softcover

ISBN 10: 331902230X ISBN 13: 9783319022307

Verlag: Springer, 2013

Inhaltsangabe

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.

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Ich bin wissenschaftlicher Mitarbeiter im Lehrgebiet Politikwissenschaft I: Staat und Regieren am Institut für Politikwissenschaft der FernUniversität in Hagen. Meine Forschungsinteressen liegen insbesondere in den Bereichen der politischen Kulturforschung und der empirischen Demokratieforschung.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 331902230X
• ISBN 13: 9783319022307
• Einband: Taschenbuch
• Anzahl der Seiten: 196
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland