A simulation study of the local linearization method for the numerical (strong) solution of stochastic differential equations driven by alpha-stable Lévy motions

A new variant of Local Linearization (LL) method is proposed for the numerical (strong) solution of differential equations driven by (additive) alpha-stable Lévy motions. This is studied through simulations making emphasis in comparison with the Euler method from the viewpoint of numerical stability. In particular, a number of examples of stiff equations are shown in which the Euler method has explosive behavior while the LL method correctly reproduces the dynamics of the exact trajectories.