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On the representation of continuous parameter processes by a sequence of random variables

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2 Author(s)

This paper examines the question of representing a continuous parameter random process { x_t, t \in T } by a sequence of random variables "without loss of information." The principal result is that such a representation by expansion coefficients relative to a basis { \phi_i } of mathcal{L}_2(T) is always possible, regardless of the orthogonality of { \phi_i } and of the boundedness of the time interval T , provided only that the process is continuous in probability and almost every sample path has finite energy.

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Information Theory, IEEE Transactions on  (Volume:16 ,  Issue: 2 )