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January 2003 Prediction of weakly stationary sequences on polynomial hypergroups
Volker Hösel, Rupert Lasser
Ann. Probab. 31(1): 93-114 (January 2003). DOI: 10.1214/aop/1046294305

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.

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Volker Hösel. Rupert Lasser. "Prediction of weakly stationary sequences on polynomial hypergroups." Ann. Probab. 31 (1) 93 - 114, January 2003. https://doi.org/10.1214/aop/1046294305

Information

Published: January 2003
First available in Project Euclid: 26 February 2003

zbMATH: 1014.60039
MathSciNet: MR1959787
Digital Object Identifier: 10.1214/aop/1046294305

Subjects:
Primary: 43A62 , 60G10 , 60G25

Keywords: Hypergroups‎ , orthogonal polynomials , prediction , Random sequences

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 1 • January 2003
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