Vectorised simulations for stochastic differential equations

Abstract

Often when solving stochastic differential equations numerically, many simulations must be generated. For example, this approach is required when computing the statistics of the numerical solution, or when verifying the strong order of convergence of a numerical method (when a range of step sizes is also required). Such computational effort can be very slow, and this paper discusses an approach to vectorise the simulation calculations and hence produce an efficient implementation. The numerical simulations here were performed in MATLAB but the techniques are equally applicable in a high performance computing environment using, for example, Fortran 90.