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dc.contributor.advisor Bradley, Richard C. en Shaw, Jason en 2010-05-24T15:11:20Z en 2027-01-24T16:11:20Z en 2010-05-31T19:15:05Z 2010-05-24T15:11:20Z en 2005 en
dc.identifier.uri en
dc.description Thesis (PhD) - Indiana University, Mathematics, 2005 en
dc.description.abstract This text first looks at sequences of discrete-indexed random fields. When these random fields satisfy certain linear dependence conditions uniformly, each will have a spectral density function (not necessarily continuous) that is bounded between two positive constants. These spectral density functions will converge in a weak sense to another function (not necessarily continuous) that is also bounded between two positive constants. Two examples will also be given that show the weak form of convergence seems to be the best one can get. An extra condition on the sequence will also be given which will ensure each spectral density function is continuous and that they uniformly converge to a continuous function. Continuous-indexed random fields will then be investigated, and linear dependence coefficients specifically for such random fields will be defined. When a selection of these linear dependence conditions are satisfied, the random field will have a continuous spectral density function. Showing this involves the construction of a special class of random fields using a standard Poisson process and the original random field. en
dc.language.iso EN en
dc.publisher [Bloomington, Ind.] : Indiana University en
dc.subject Probability Theory en
dc.subject spectral densities en
dc.subject random field en
dc.subject weak dependence en
dc.subject.classification Mathematics en
dc.title Spectral densities of discrete and continuous-indexed random fields en
dc.type Doctoral Dissertation en

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