On the existence and the applications of modified equations for stochastic differential equations
On the existence and the applications of modified equations for stochastic differential equations
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 an 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.
102-130
Zygalakis, K. C.
a330d719-2ccb-49bd-8cd8-d06b1e6daca6
2011
Zygalakis, K. C.
a330d719-2ccb-49bd-8cd8-d06b1e6daca6
Zygalakis, K. C.
(2011)
On the existence and the applications of modified equations for stochastic differential equations.
SIAM Journal on Scientific Computing, 33 (1), .
(doi:10.1137/090762336).
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 an 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.
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Published date: 2011
Organisations:
Applied Mathematics
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Local EPrints ID: 340547
URI: http://eprints.soton.ac.uk/id/eprint/340547
ISSN: 1064-8275
PURE UUID: 23848c58-69cd-4bdf-adcc-a21a07d7b36c
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Date deposited: 26 Jun 2012 10:25
Last modified: 14 Mar 2024 11:26
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K. C. Zygalakis
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