Consistent Systemsof Finite Dimensional Distributions

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Submitted: 2024-12-18; Published: 2024-12-18

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Abstract

In the paper we discuss the problem of descriptionof random fields by means of systems of finite dimensional prob-ability distributions.We present from a unified point of view a survey of the varioussuch systems associated with random fields.Then general system of finite dimensional distributions with asuitable consistency condition is introduced. The properties, re-lations with other systems, as well as the problems of existenceand uniqueness of the corresponding random fields are discussed.