The Mathematical Institute, University of Oxford, Eprints Archive

On the existence and the applications of
modified equations for stochastic differential
equations

Zygalakis, K. C. (2009) On the existence and the applications of
modified equations for stochastic differential
equations.
Not specified . (Submitted)

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Abstract

In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive a SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed.

Item Type:Article
Subjects:H - N > Numerical analysis
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:816
Deposited By:Dr M. Stoll
Deposited On:24 Sep 2009 13:37
Last Modified:24 Sep 2009 13:37

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