We consider the Euler scheme for stochastic differential equations with
jumps, whose intensity might be infinite and the jump structure may depend on
the position. This general type of SDE is explicitly given for Feller processes
and a general convergence condition is presented.
In particular the characteristic functions of the increments of the Euler
scheme are calculated in terms of the symbol of the Feller process in a closed
form. These increments are increments of L\'evy processes and thus the Euler
scheme can be used for simulation by applying standard techniques from L\'evy
processes
