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Abstract
This paper applies several wellknown tricks from
the numerical treatment of deterministic differential
equations to improve the efficiency of the multilevel
Monte Carlo (MLMC) method for stochastic diffe
rential equations (SDEs) and especially the Langevin
equation. We use modified equations analysis as an
alternative to strongapproximation theory for the
integrator, and we apply this to introduce MLMC for
Langevintype equations with integrators based on
operator splitting. We combine this with extrapolation
and investigate the use of discrete random variables
in place of the Gaussian increments, which is a
wellknown technique for the weak approximation
of SDEs. We show that, for smallnoise problems,
discrete random variables can lead to an increase
in efficiency of almost two orders of magnitude for
practical levels of accuracy.
Original language  English 

Number of pages  20 
Journal  Proceedings of the Royal Society A 
Volume  471 
Issue number  2176 
Early online date  18 Mar 2015 
DOIs  
Publication status  Published  Apr 2015 
Keywords
 numericalsolutionofstochasticdifferential equations,modifiedequations,geometrical integrators,weakapproximation, extrapolation
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 1 Finished

Phase 2 Scalability of Elliptic Solvers in Weather and Climate Modelling
Scheichl, R.
Natural Environment Research Council
24/06/13 → 30/06/16
Project: Research council