Convergence of Euler-Maruyama Method for Stochastic Differential Equations Driven by alpha-stable Levy Motion

Abstract

In the literature, the Euler-Maruyama (EM) method for approximation purposes of stochastic differential Equations (SDE) driven by alph

-stable Levy motions is reported. Convergence in probability of this method was proven but it is surrounded by some ambiguities. To accomplish the method without ambiguities, this article has derived convergence in probability of numerical EM method based on diffusion given by semimartingales for SDEs driven by alpha-stable processes. Some examples are provided, their numerical solution are obtained and theoretical results are reconfirmed. The  adopted method could be applied to other subclasses of semimartingales.