On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes

SDE driven by an $\alpha$-stable process, $\alpha \in [1,2),$ with Lipshitz continuous coefficient and $\beta$-H"older drift is considered. The existence and uniqueness of a strong solution is proved when $\beta >1-\alpha /2$byshowingthatitis$L_{p}$-limitofEulerapproximations\mathrm{.}The$L_{p}$-error (rate of convergence) is obtained for a nondegenerate truncated and nontruncated driving process. The rate in the case of Lipshitz continuous coefficients is derived as well.