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Existence of moments in a stationary stochastic difference equation

Published online by Cambridge University Press:  01 July 2016

Hans Arnfinn Karlsen
Hans Arnfinn Karlsen*
Affiliation:
University of Bergen
*
∗Postal address: Department of Mathematics, University of Bergen, 5007-Bergen, Norway.
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Abstract

The stationary stochastic difference equation Xt = YtXt–1 + Wt is analyzed with emphasis on conditions ensuring that ||Xt||p <∞. Some general results are obtained and then applied to different classes of input processes {(Yt, Wt)}. Especially both necessary and sufficient conditions are given in the Gaussian case. We also obtain results concerning moments of products of dependent variables.

Keywords

DOUBLY STOCHASTIC PROCESSESMOMENTS OF PRODUCTS OF DEPENDENT VARIABLESNON-LINEAR TIME SERIESGAUSSIAN INEQUALITIES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 129 - 146
Copyright
Copyright © Applied Probability Trust 1990 

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