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Pre-Publicación 2013-08

Hernán Mardones, Carlos M. Mora:

Stable numerical methods for two classes of SDEs with multiplicative noise: bilinear and scalar

Abstract:

We develop new numerical schemes for bilinear systems of stochastic differential equations (SDEs). To this end, we present a new methodology for solving stiff multidimensional SDEs with multiplicative noise, as well as, we introduce a new stable numerical method for non-linear scalar SDEs. The rate of weak convergence of the new schemes is linear. Moreover, they preserve the possible exponential stability of the unknown solutions for any step-size. Four numerical experiments illustrate the good performance of the proposed algorithms.

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