Abstract
In this paper, we get some convergence rates in total variation distance in approximating discretized paths of Lévy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.
Funding Statement
This research is partially supported by the PRC EFFI, funded by French ANR, reference ANR-21-CE40-0021-02.
Acknowledgements
The author would like to thank the anonymous referees for their constructive comments that improved the quality of this paper.
Citation
Emmanuelle Clément. "Hellinger and total variation distance in approximating Lévy driven SDEs." Ann. Appl. Probab. 33 (3) 2176 - 2209, June 2023. https://doi.org/10.1214/22-AAP1863
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