Statistical causality and separable processes

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 causal...

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Bibliographic Details
Published in:Statistics & probability letters 2020-12, Vol.167, p.108915, Article 108915
Main Authors: Valjarević, Dragana, Petrović, Ljiljana
Format: Article
Language:English
Subjects:
Causality
Filtration
Separable [formula omitted]-algebra
Separable process
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Summary: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 Lp(Ω,G∞,P) to be separable. The concept of statistical causality is related to the notion separability of stochastic processes, too.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2020.108915