Power series with i.i.d. coefficients

Barry C. Arnold and Krishna B. Athreya

Statistics & Probability Letters, 2013, vol. 83, issue 3, 923-929

Abstract: 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.

Keywords: Long run distribution; Convolution; Markov chain; Weak closure; Self-decomposable (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.11.031

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