The Euler-Maruyama method for S(F)DEs with Hölder drift and α-stable noise

ABSTRACT

Consider the stochastic (functional) differential equations in with Hölder continuous drift driven by α-stable process satisfying (H1). Using Zvonkin type transformation, the convergence rate of Euler-Maruyama method is obtained. The results are new, especially for the functional SDEs with irregular drift.

KEYWORDS:

• Hölder continuous
• Zvonkin type transformation
• Euler-Maruyama method
• α-stable process.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60H35
• 41A25
• 60H10
• 60C30

Acknowledgement

The authors would like to thank Professor Feng-Yu Wang for edits and helpful comments.

Funding

This research is supported by National Nature Science Foundation of China (grant no. 11701588).