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Sampling and reconstruction for shift-invariant stochastic processes

In this paper, combining stochastic processes with shift-invariant spaces, we introduce shift-invariant stochastic processes. It is a general case of the classical band-limited stochastic processes and a kind of non-band-limited stochastic processes. Two sampling theorems are obtained for the shift-invariant stochastic processes. The results for band-limited stochastic processes and shift-invariant spaces are generalized by our new results.