Power series with i.i.d. coefficients

Arnold, Barry C. ; Athreya, Krishna B. (2013) Power series with i.i.d. coefficients Statistics & Probability Letters, 83 (3). pp. 923-929. ISSN 01677152

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Official URL: http://doi.org/10.1016/j.spl.2012.11.031

Related URL: http://dx.doi.org/10.1016/j.spl.2012.11.031


In this work we consider a power series of the form X=∑j=0∞δjZj where 0<δ<10<δ<1 and {Zj}j≥0{Zj}j≥0 is an i.i.d. sequence of random variables. We show that XX is well-defined iff E[(log|Z0|)+]<∞E[(log|Z0|)+]<∞ and establish a number of properties of the distribution of XX, such as continuity and closure under convolution and weak convergence.

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