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

R. Mikulevicius; Fanhui Xu

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arXiv · 1608.02303

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

R. Mikulevicius·Fanhui Xu

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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.

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BibTeX RIS

R. Mikulevicius, Fanhui Xu. 2016-08-08. On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes. https://arxiv.org/abs/1608.02303

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