Equivalence Between Representations for Samplable Stochastic Processes and its Relationship With Riesz Bases

We characterize random signals which can be linearly determined by their samples. This problem is related to the question of the representation of random variables by means of a countable Riesz basis. We study different representations for processes which are linearly determined by a countable Riesz basis. This concerns the representation of continuous time processes by means of discrete samples.