Bimeasures and sampling theorems for weakly harmonizable processes

Authors: Derek K. Chang ^a; M. M. Rao ^a

Affiliation:

^a Department of Mathematics, University of California, Riverside, Califorina

DOI: 10.1080/07362998308809003

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 1, Issue 1 1983 , pages 21 - 55

Subjects: Statistics & Probability; Stochastic Models & Processes;

Formats available: PDF (English)

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Abstract

x(t),t∈R

a weakly harmonizable process,conditions on the process are found in order that ./LSAA_A_8809003_O_XML_IMAGES/LSAA_A_8809003_O_ILM0001.gif

for a suitable agr

>O and coefficient a_n(t),the series converging in L²(P)-mean.Consequently the process can be determined by sampling at fixed intervals nh ./LSAA_A_8809003_O_XML_IMAGES/LSAA_A_8809003_O_ILM0002.gif

./LSAA_A_8809003_O_XML_IMAGES/LSAA_A_8809003_O_ILM0002.gif

. A corresponding result is also obtained for a more general cram eacute

er class.To carry out this analysis,it is necessary to use the properties of bimeasures. Some aspects of the bimeasure theory and its distinction from the Lebesgue theory are included. This is used essentially for the analysis of harmonizable processes, and has independent interest

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Bimeasures and sampling theorems for weakly harmonizable processes

Abstract