随机微分方程驯服指数积分器的弱收敛性

IF 1.6 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

BIT Numerical Mathematics Pub Date : 2024-07-11 DOI:10.1007/s10543-024-01029-6

Utku Erdoğan, Gabriel J. Lord

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引用次数: 0

摘要

我们证明了一类基于指数的积分器对具有非全局 Lipschitz 漂移的 SDE 的一阶弱收敛性。我们的分析涵盖了基于几何布朗运动（GBM）方法的驯化版本以及标准指数方案。通过四种不同的多级蒙特卡洛技术，我们对 GBM 和指数驯化方法的数值性能进行了比较。我们发现，与 GBM 驯化法不同，对于线性噪声，标准指数驯化法需要严格限制步长。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Weak convergence of tamed exponential integrators for stochastic differential equations

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Weak convergence of tamed exponential integrators for stochastic differential equations

We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschitz drift. Our analysis covers tamed versions of Geometric Brownian Motion (GBM) based methods as well as the standard exponential schemes. The numerical performance of both the GBM and exponential tamed methods through four different multi-level Monte Carlo techniques are compared. We observe that for linear noise the standard exponential tamed method requires severe restrictions on the step size unlike the GBM tamed method.

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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.