A direct inversion formula for SFT
A direct inversion formula for SFT
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SFT的直接反演公式
DOI：
10.1007/s13171-014-0056-1
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Shigeyoshi Ogawa
中科院分区：
文献类型：
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作者：
OGAWA,S. & UEMURA,H.;Shigeyoshi Ogawa
本文研究随机函数f（t，ω）是否以及如何由它的SFT（即随机傅立叶变换）象唯一确定的问题。这个问题首先由作者在随机分析的各种问题的研究中提出（Ogawa 1979，1985），最近在Ogawa（1986），Ogawa和Uemura（2013，2014）的论文中再次研究，其中对这个问题给出了一些肯定的答案以及SFT反演的方案。在这些文件中的问题已经研究的框架内的齐次混沌，我们感到笨拙的一部分，因为有所有的声明和计划的反演表示的无限序列的代表内核的给定维纳功能，部分是因为执行反演计划的发展，我们需要完整的数据的基础布朗运动。本说明的目的是显示一个基本的方法来解决这个问题，不依赖于这样沉重的框架，如均匀混沌，并给出一个直接的公式反演的SFT。
We are concerned with the question whether and how a random functionf(t,ω) can be uniquely determined by its image of SFT (i.e. stochastic Fourier transformation). The question was first posed by the author in the study of various problems of stochastic analysis (Ogawa 1979, 1985) and has been studied again recently in the papers Ogawa (1986), Ogawa and Uemura (2013, 2014) where some affirmative answers to the question as well as the schemes for inversion of SFT are given. In these papers the problem has been studied in the framework of Homogeneous Chaos which we feel clumsy partly because there all statements and schemes for the inversion are expressed in terms of the infinite sequence of representing kernels of the given Wiener functional and partly because for the execution of the inversion scheme developed there we need complete data of the underlying Brownian motion. The aim of the present note is to show an elementary approach to the problem, that does not rely on such heavy frameworks like Homogeneous Chaos, and give a direct formula for the inversion of the SFT.