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Existence of moments in a stationary stochastic difference equation
Hans Arnfinn Karlsen
Journal:

Advances in Applied Probability / Volume 22 / Issue 1 / March 1990

Published online by Cambridge University Press:

01 July 2016, pp. 129-146

Print publication:

March 1990
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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.

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Existence of moments in a stationary stochastic difference equation