Hernán Mardones, Carlos M. Mora:
Stable numerical methods for two classes of SDEs with multiplicative noise: bilinear and scalar
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.