Abstract/Details

Spectral densities of discrete and continuous-indexed random fields


2005 2005

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Abstract (summary)

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.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Continuous-indexed random fields; Discrete-indexed random fields; Probability theory; Random fields; Spectral densities
Title
Spectral densities of discrete and continuous-indexed random fields
Author
Shaw, Jason
Number of pages
62
Publication year
2005
Degree date
2005
School code
0093
Source
DAI-B 66/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
0542308002, 9780542308000
Advisor
Bradley, Richard C.
University/institution
Indiana University
University location
United States -- Indiana
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3183490
ProQuest document ID
304987333
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304987333
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