具有不连续漂移的跳跃-扩散 SDE 的误差下限和近似最优性

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

BIT Numerical Mathematics Pub Date : 2024-09-09 DOI:10.1007/s10543-024-01036-7

Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi

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引用次数: 0

摘要

本文证明了具有不连续漂移的跳跃扩散随机微分方程（SDE）数值方法的尖锐误差下限。本文研究了用非自适应和跳变自适应近似方案对跳跃扩散随机微分方程的近似，并为这两类近似方案提供了 3/4 阶的误差下限。由此得出了基于变换的跳变适应准米尔斯坦方案的最优性。

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

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.

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来源期刊

BIT Numerical Mathematics 数学-计算机：软件工程

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The journal BIT has been published since 1961. BIT publishes original research papers in the rapidly developing field of numerical analysis. The essential areas covered by BIT are development and analysis of numerical methods as well as the design and use of algorithms for scientific computing. Topics emphasized by BIT include numerical methods in approximation, linear algebra, and ordinary and partial differential equations.