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On Band Limited Stochastic Processes
Alan J. Lee
SIAM Journal on Applied Mathematics
Vol. 30, No. 2 (Mar., 1976), pp. 269-277
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2100528
Page Count: 9
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Using a modification of a technique of Zakai, the notion of a band limited stochastic process is extended to the class of second order measurable mean square continuous processes whose covariances are polynomially bounded. The connections between such processes and a class of processes considered by Piranashvili are explored and these two classes are shown to be essentially the same. Such processes are shown to satisfy a modified form of the sampling theorem, have representations in terms of harmonizable processes, and admit orthogonal series representations with band limited coefficient functions.
SIAM Journal on Applied Mathematics © 1976 Society for Industrial and Applied Mathematics