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Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift (2303.05945v3)
Published 10 Mar 2023 in math.NA and cs.NA
Abstract: 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.