SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Solving Stiff Stochastic Differential Equations with a Stabilized Multilevel Monte Carlo Method

A. Blumenthal and A. Abdulle

Abstract
We introduce a new stabilized multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales, problems that we call stiff. Due to time stepsize restriction on the fastest scales, not all levels of the standard MLMC approach based on classical explicit methods can be exploited, and thus, the performance of such MLMC methods deteriorates. Turning to explicit stabilized numerical integrators [1] and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of MLMC methods, we show that the computational complexity for stiff systems is significantly reduced. The computational algorithm of this new stabilized MLMC method remains fully explicit and easy to implement [2].

Bibliography
[1] A. Abdulle and T. Li, S-ROCK methods for stiff Itô SDEs, Commun. Math. Sci., 6(4):845-868, 2008.
[2] A. Abdulle and A. Blumenthal, Stabilized Multilevel Monte Carlo Method for Stiff Stochastic Differential Equations, submitted to publication, 2013.

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