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Random Fields with Pólya Correlation Structure

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Richard Finlay  and
Eugene Seneta
Richard Finlay*
Affiliation:
University of Sydney
Eugene Seneta*
Affiliation:
University of Sydney
*
∗ Postal address: School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW 2006, Australia.
∗ Postal address: School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW 2006, Australia.
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Abstract

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We construct random fields with Pólya-type autocorrelation function and dampened Pólya cross-correlation function. The marginal distribution of the random fields may be taken as any infinitely divisible distribution with finite variance, and the random fields are fully characterized in terms of their joint characteristic function. This makes available a new class of non-Gaussian random fields with flexible correlation structure for use in modeling and estimation.

Keywords

Random fieldinfinitely divisible distributionPólya autocorrelation

MSC classification

Primary: 60G60: Random fields
Secondary: 60G10: Stationary processes 60E07: Infinitely divisible distributions; stable distributions
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 1037 - 1050
Copyright
© Applied Probability Trust 

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