Power series with i.i.d. coefficients

In this work we consider a power series of the form X=∑j=0∞δjZj where 0<δ<1 and {Zj}j≥0 is an i.i.d. sequence of random variables. We show that X is well-defined iff E[(log|Z0|)+]<∞ and establish a number of properties of the distribution of X, such as continuity and closure under convolution and weak convergence.

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Year of publication:	2013
Authors:	Arnold, Barry C. ; Athreya, Krishna B.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 3, p. 923-929
Publisher:	Elsevier
Subject:	Long run distribution \| Convolution \| Markov chain \| Weak closure \| Self-decomposable

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040083