论文标题
普遍的fock空间和时刻
Generalized Fock space and moments
论文作者
论文摘要
在本文中，我们开发了一个框架，以将HIDA白噪声空间中的广义随机过程理论扩展到更通用的概率空间，包括灰噪声空间。为了获得Wiener-Itô扩展，我们将其作为瞬间问题重新提出，并明确计算矩。在这种情况下，我们进一步展示了一个称为强代代数的拓扑代数家族的重要性。此外，我们还显示了我们方法对随机过程研究的适用性。
In this paper we develop a framework to extend the theory of generalized stochastic processes in the Hida white noise space to more general probability spaces which include the grey noise space. To obtain a Wiener-Itô expansion we recast it as a moment problem and calculate the moments explicitly. We further show the importance of a family of topological algebras called strong algebras in this context. Furthermore we show the applicability of our approach to the study of stochastic processes.
