APPROXIMATION OF FELLER PROCESSES BY MARKOV CHAINS WITH LÉVY INCREMENTS

Abstract

We consider Feller processes whose generators have the test functions as an operator core. In this case, the generator is a pseudo differential operator with negative definite symbol q(x, ξ). If |q(x, ξ)| < c(1 + |ξ| 2 ), the corresponding Feller process can be approximated by Markov chains whose steps are increments of Lévy processes. This approximation can easily be used for a simulation of the sample path of a Feller process. Further, we provide conditions in terms of the symbol for the transition operators of the Markov chains to be Feller. This gives rise to a sequence of Feller processes approximating the given Feller process.