The Annals of Probability

Prediction of weakly stationary sequences on polynomial hypergroups

Volker Hösel and Rupert Lasser

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Abstract

We investigate random sequences $(X_n)_{\nin_0}$ with spectral representation based on certain orthogonal polynomials, that is, random sequences that are weakly stationary with respect to polynomial hypergroups. We present various situations where one meets this kind of sequence. The main topic is on the one-step prediction. In particular, it is examined when the mean-squared error tends to zero. For many cases we present a complete solution for the problem of $(X_n)_{\nin_0}$ being asymptotically deterministic.

Article information

Source
Ann. Probab., Volume 31, Number 1 (2003), 93-114.

Dates
First available in Project Euclid: 26 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1046294305

Digital Object Identifier
doi:10.1214/aop/1046294305

Mathematical Reviews number (MathSciNet)
MR1959787

Zentralblatt MATH identifier
1014.60039

Subjects
Primary: 60G10: Stationary processes 60G25: Prediction theory [See also 62M20] 43A62: Hypergroups

Keywords
Prediction random sequences orthogonal polynomials hypergroups

Citation

Hösel, Volker; Lasser, Rupert. Prediction of weakly stationary sequences on polynomial hypergroups. Ann. Probab. 31 (2003), no. 1, 93--114. doi:10.1214/aop/1046294305. https://projecteuclid.org/euclid.aop/1046294305


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