Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Becker Sebastian; Gess Benjamin; Jentzen Arnulf; Kloeden Peter E.

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Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

机译：用于随机热方程数值近似的强近似误差的下限和上限

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摘要

This article establishes optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise. Thereby, this work proves the optimality of the strong convergence rates for certain full-discrete approximations of stochastic Allen-Cahn equations with space-time white noise which have been obtained in a recent previous work of the authors of this article.

机译：本文建立了通过时空白噪声驱动的随机热方程的强全离散数值近似的最佳上下误差估计。由此，该工作证明了具有在本文最近一项工作的时空白噪声的时断艾伦-CAHN方程对随机艾伦-CAHN方程的某些全离散近似的最佳收敛速率。

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来源
《BIT numerical mathematics》 |2020年第4期|1057-1073|共17页
作者
Becker Sebastian; Gess Benjamin; Jentzen Arnulf; Kloeden Peter E.;
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作者单位

Swiss Fed Inst Technol Dept Math RiskLab CH-8092 Zurich Switzerland;

Max Planck Inst Math Sci D-04103 Leipzig Germany|Univ Bielefeld Fac Math D-33615 Bielefeld Germany;

Swiss Fed Inst Technol Dept Math SAM CH-8092 Zurich Switzerland|Univ Munster Fac Math & Comp Sci D-48149 Munster Germany;

Goethe Univ Frankfurt Math Inst D-60325 Frankfurt Germany;

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原文格式 PDF
正文语种 eng
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关键词
Upper and lower error estimates; Stochastic heat equation; Space-time white noise;

机译：上下误差估计;随机热方程;时空白噪声;

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1. Lower Bounds and Nonuniform Time Discretization for Approximation of Stochastic Heat Equations [J] . Thomas Muller-Gronbach, Klaus Ritter Foundations of computational mathematics . 2007,第2期

机译：随机热方程的下界和非均匀时间离散
2. Lower Bounds and Nonuniform Time Discretization for Approximation of Stochastic Heat Equations [J] . Thomas Muller-Gronbach, Klaus Ritter Foundations of Computational Mathematics . 2007,第2期

机译：随机热方程的下界和非均匀时间离散
3. The Strong Convergence and Numerical Stability of Multistep Approximations of Solutions of Stochastic Ordinary Differential Equations [J] . Rozsa Horvath-Bokor Stochastic Analysis and Applications . 2007,第1期

机译：随机常微分方程解的多步逼近的强收敛性和数值稳定性
4. Saddlepoint approximations of lower and upper bounds to the error probability in channel coding [C] . Josep Font-Segura, Gonzalo Vazquez-Vilar, Alfonso Martinez, Annual Conference on Information Sciences and Systems . 2018

机译：信道编码中错误概率上下界的鞍点近似
5. Numerical approximations of stochastic differential equations with applications to mathematical neurosciences [D] . Rahman, Mohammad Mahbubur 2004

机译：随机微分方程的数值逼近及其在数学神经科学中的应用
6. On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions [O] . Máté Gerencsér, Arnulf Jentzen, Diyora Salimova -1

机译：具有二维空间强逼近的具有任意慢收敛速度的随机微分方程
7. Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations [O] . de Naurois, Ladislas Jacobe, Jentzen, Arnulf, Welti, Timo 2017

机译：空间谱Galerkin的弱近似误差的下界随机波动方程的近似
8. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. [R] . Trenchea, C. 2012

机译：基于高维随机偏微分方程解的跟踪统计量的有效数值逼近。

Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

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