谱随机积分的测度变换
概率论
2020-06-15 v2
摘要
在温和条件下，仅从近乎纯粹的测度论考量出发，且无需具体提及随机过程，即可获得一个类似于通常Radon-Nikodým测度变换的测度变换结果，该结果与协方差平稳过程谱表示的随机积分变体相关联；相关思想自然嵌入于 空间的希尔伯特空间理论中。旨在给出的主要贡献，包括谱随机积分测度变换的完整证明，是面向测度变换的谱随机积分精炼且自包含的发展。
引用
@article{arxiv.2006.05834,
title = {Change of Measures for Spectral Stochastic Integrals},
author = {Yu-Lin Chou},
journal= {arXiv preprint arXiv:2006.05834},
year = {2020}
}
备注
Two slight but not insubstantial improvements to increase clarity, adding back the missing word "disjoint" to the definition of an orthogonal elementary stochastic measure, and deleting some out-of-context words regarding $\mathscr{A}$-simple functions