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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Basic Concepts of Numerical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods
verfasst von : Henri Schurz
Erschienen in: Stochastic Differential Equations and Processes
Verlag: Springer Berlin Heidelberg
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We present the comprehensive concept of dynamic consistency of numerical methods for (ordinary) stochastic differential equations. The concept is illustrated by the well-known class of balanced drift-implicit stochastic Theta methods and relies on several well-known concepts of numerical analysis to replicate the qualitative behaviour of underlying continuous time systems under adequate discretization. This involves the concepts of consistency, stability, convergence, positivity, boundedness, oscillations, contractivity and energy behaviour. Numerous results from literature are reviewed in this context.