The Euler scheme for Lévy driven stochastic differential equations
The paper considers the discrete time approximation of the solution of a stochastic differential equation that is driven by a Lévy process. It is shown that the Euler approximation converges under appropriate conditions in a weak sense to the solution of the given stochastic differential equation. If the Lévy measure has finite moments up to a certain order, then the typical rate of weak convergence has been shown. Otherwise the rate of convergence turns out to be smaller. The suggested Euler method is useful for Monte-Carlo simulation of solutions of specific integro-differential equations.
scientific article; zbMATH DE number 1018395
scientific article