A Simulation Study of the Local Linearization Method for the Numerical (strong) Solution of Stochastic Differential Equations Driven by Alpha-stable Lévy Motions
نویسندگان
چکیده
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. RESUMEN. Se propone una nueva variante del método de Linealización Local (LL) para la solución (fuerte) de ecuaciones diferenciales con respecto a procesos de Lévy alfa-estables (aditivo). A través de simulaciones se estudia el método comparación con el método de Euler desde el punto de vista de la estabilidad numérica. En particular, a partir de un número de ecuaciones rígidas (“stiff”), se muestra que el método de Euler tiene un comportamiento explosivo mientras que el método LL reproduce correctamente la dinámica de las trayectorias exactas.
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