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

R. Mikulevicius; Fanhui Xu

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

Probability 2016-08-09 v1 Analysis of PDEs

Authors: R. Mikulevicius , Fanhui Xu

Abstract

SDE driven by an $\alpha$ -stable process, $\alpha \in \lbrack 1,2),$ with Lipshitz continuous coefficient and $\beta$ -H\"older drift is considered. The existence and uniqueness of a strong solution is proved when $\beta >1-\alpha /2$ by showing that it is $L_{p}$ -limit of Euler approximations. 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.

Keywords

stochastic differential equations Lévy processes Euler approximation rate of convergence strong solution Hölder drift Lipshitz coefficient

Cite

@article{arxiv.1608.02303,
  title  = {On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes},
  author = {R. Mikulevicius and Fanhui Xu},
  journal= {arXiv preprint arXiv:1608.02303},
  year   = {2016}
}

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