Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift
Numerical Analysis
2023-12-06 v3 Numerical Analysis
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 for both classes of approximation schemes. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.
Cite
@article{arxiv.2303.05945,
title = {Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift},
author = {Paweł Przybyłowicz and Verena Schwarz and Michaela Szölgyenyi},
journal= {arXiv preprint arXiv:2303.05945},
year = {2023}
}