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 non-Gaussian stochastic processes.

中文翻译：

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广义白噪声分析和拓扑代数

在本文中，我们开发了一个框架，将 Hida 白噪声空间中的广义随机过程理论扩展到包括灰色噪声空间在内的更一般的概率空间。为了获得 Wiener-Itô 展开，我们将其重铸为矩问题并明确计算矩。我们进一步展示了在这种情况下称为强代数的拓扑代数族的重要性。此外，我们展示了我们的方法对非高斯随机过程研究的适用性。