A SIMULATION STUDY OF THE LOCAL LINEARIZATION METHOD FOR THE NUMERICAL (STRONG) SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY ALPHA-STABLE LÉVY MOTIONS
Keywords:Stochastic Differential Equations, Local Linearization Method, Stable Distributions, Lévy Process, Numerical Stability
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
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