Abstract In this paper we consider the statistical concept for continuous-time stochastic processes, which is based on Granger’s definition of causality. We, also, show that separability is directly related to causality concepts. More precisely, we provide necessary conditions, in terms of statistical causality, for the space L p ( Ω , G ∞ , P ) to be separable. The concept of statistical causality is related to the notion separability of stochastic processes, too.

中文翻译：

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统计因果关系和可分离过程

摘要 在本文中，我们考虑了基于格兰杰因果关系定义的连续时间随机过程的统计概念。我们还表明可分离性与因果关系概念直接相关。更准确地说，我们在统计因果关系方面为空间 L p ( Ω , G ∞ , P ) 可分提供了必要条件。统计因果关系的概念也与随机过程的可分离性概念有关。