Nonhomogeneous Noise and Q-Wiener Processes on Bounded Domains
Nonhomogeneous Noise and Q-Wiener Processes on Bounded Domains
复制标题
有界域上的非齐次噪声和 Q-Wiener 过程
DOI：
10.1081/sap-200050092
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
D. Blömker
中科院分区：
文献类型：
--
作者：
D. Blömker
摘要在这篇文章中，我们评论的噪声和Q-维纳过程之间的众所周知的连接。在物理应用中，噪声通常被给定为广义高斯过程，并且所有的假设都用相关泛函来表示。相比之下，有界域上的随机偏微分方程的数学理论在许多情况下是用Q-Wiener过程来表述的。我们的目的是将对协方差算子Q的频繁假设与对噪声过程的相关函数的假设联系起来，噪声过程的相关函数是Q的核。我们的一个主要结果给出了当Wiener过程作为Laplacian特征函数的级数展开时的充要条件。
Abstract In this article, we comment on the well known connection between noise and Q-Wiener processes. In physical applications, noise is usually given as a generalized Gaussian process and all assumptions are formulated in terms of the correlation functional. In contrast, the mathematical theory of stochastic partial differential equations on bounded domains is in many cases formulated with Q-Wiener processes. Our aim is to relate frequently made assumptions on the covariance operator Q to assumptions on the correlation function of the noise process, which is the kernel of Q. One of our main results gives necessary and sufficient conditions when the Wiener process is given as a series expansion in terms of eigenfunctions of the Laplacian.