The Annals of Probability

Stationary random fields with linear regressions

Włodzimierz Bryc

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Abstract

We analyze and identify stationary fields with linear regressions and quadratic conditional variances. We give sufficient conditions to determine one-dimensional distributions uniquely as normal and as certain compactly supported distributions. Our technique relies on orthogonal polynomials, which under our assumptions turn out to be a version of the so-called continuous q-Hermite polynomials.

Article information

Source
Ann. Probab., Volume 29, Number 1 (2001), 504-519.

Dates
First available in Project Euclid: 21 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aop/1008956342

Digital Object Identifier
doi:10.1214/aop/1008956342

Mathematical Reviews number (MathSciNet)
MR1825162

Zentralblatt MATH identifier
1014.60013

Subjects
Primary: 60E99: None of the above, but in this section
Secondary: 60G10: Stationary processes

Keywords
Conditional moments hypergeometric orthogonal polynomials q-Hermite polynomials q -Gaussian processes linear regression

Citation

Bryc, Włodzimierz. Stationary random fields with linear regressions. Ann. Probab. 29 (2001), no. 1, 504--519. doi:10.1214/aop/1008956342. https://projecteuclid.org/euclid.aop/1008956342


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References

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