Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

03/10/2023

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by   Paweł Przybyłowicz, et al.

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In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes and provide lower error bounds of order 3/4 for both classes of approximation schemes. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.