Abstract
We consider the class of random processes having linear shift operators. This class is an extension of the class of wide-sense stationary processes (which have unitary shift operators). Conditions for a process to have linear shifts are formulated in terms of the covariance function of the process. Sufficient conditions for a purely nondeterministic process to have linear shifts are given. Theorems concerning superposition, products, and linear transformations of such processes are proved, and applications are indicated. A comparison with the class of locally stationary processes is made. The essential concepts involved are also extended to generalized random processes.
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