带乘性噪声的半线性抛物型随机偏微分方程的路径空间逼近
数值分析
2018-12-19 v1
摘要
我们给出了希尔伯特空间中带乘性噪声的半线性随机微分方程空间逼近的收敛速率。我们考虑的空间逼近为谱 Galerkin 与有限元，所考虑的收敛类型为强收敛与几乎必然一致收敛，即路径wise收敛。证明基于先前发表的此类方程的扰动结果。
引用
@article{arxiv.1812.07419,
title = {Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise},
author = {Sonja Cox and Erika Hausenblas},
journal= {arXiv preprint arXiv:1812.07419},
year = {2018}
}
备注
This article was published in the International Journal of Computer Mathematics in December 2012. However, the proof of Proposition 4.2 in the published article contained a mistake in the final estimate. This mistake is repaired in the arXiv submission (see Proposition 4.1), all changes with respect to the published article are marked red. The mistake did not affect the main results