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

Abstract

A SDE driven by an -stable process, with a Lipshitz continuous coefficient and a -Hölder drift is considered. The existence and uniqueness of a strong solution is proved when by showing that it is the -limit of Euler approximations. The -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.

Keywords:

• Strong solutions
• Levy processes
• strong approximation

Acknowledgements

We are very grateful to our reviewer for valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.