On upper and lower bounds for pathwise approximation of scalar SDEs with reflection

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2025-05-16 DOI:10.1016/j.jco.2025.101959

Mario Hefter , André Herzwurm , Klaus Ritter

引用次数: 0

Abstract

For scalar SDEs with a one-sided reflection we study pathwise approximation, globally on a compact time interval or at a single time point. We consider algorithms based on sequential evaluations of the driving Brownian motion and establish upper and lower bounds for the minimal errors. Exploiting the relation to a reflected Ornstein-Uhlenbeck process, we also provide a new upper bound for a Cox-Ingersoll-Ross process.

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带反射的标量SDEs路径逼近的上界和下界

对于具有单侧反射的标量SDEs，我们研究了在紧时间区间上的全局路径逼近和在单个时间点上的全局路径逼近。我们考虑基于驱动布朗运动的顺序评估的算法，并建立最小误差的上界和下界。利用与反射的Ornstein-Uhlenbeck过程的关系，我们还为Cox-Ingersoll-Ross过程提供了一个新的上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.