Przybyłowicz Paweł, Schwarz Verena, Szölgyenyi Michaela
Faculty of Applied Mathematics, AGH University of Krakow, Al. Mickiewicza 30, 30-059 Krakow, Poland.
Department of Statistics, University of Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt, Austria.
BIT Numer Math. 2024;64(4):35. doi: 10.1007/s10543-024-01036-7. Epub 2024 Sep 9.
In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes is studied and lower error bounds of order 3/4 for both classes of approximation schemes are provided. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.
本文证明了具有不连续漂移的跳扩散随机微分方程（SDEs）数值方法的精确低误差界。研究了具有非自适应以及跳适应近似格式的跳扩散SDEs的近似，并给出了这两类近似格式的3/4阶低误差界。这使得基于变换的跳适应拟米尔斯坦格式具有最优性。
