The Local Linearization Method for Numerical Integration of Random Differential Equations

A Local Linearization (LL) method for the numerical integration of Random Differential Equations (RDE) is introduced. The classical LL approach is adapted to this type of equations, which are defined by random vector fields that are typically at most Hölder continuous with respect to the time argument. The order of strong convergence of the method is studied. It turns out that the LL method improves the order of convergence of conventional numerical methods that have been applied to RDEs. Additionally, the performance of the LL method is illustrated by means of numerical simulations, which show that it behaves well even in those equations with complicated noisy dynamics where conventional methods fail.AMS subject classification (2000) 34F05, 34K28, 60H25.H. Cruz: This work was partially supported by the Research Grant 03-059 RG/MATHS/LA from the Third World Academic of Science (TWAS).Received July 2004. Accepted October 2004. Communicated by Anders Szepessy.