On types of distributions of sums of one class of random power series with independent identically distributed coefficients

1999 ◽  
Vol 51 (1) ◽  
pp. 140-145 ◽  
Author(s):  
A. A. Litvinyuk
Keyword(s):  
Power Series ◽  
Random Power Series ◽  
Independent Identically Distributed

scholarly journals Random Power Series in Q p , 0 Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Haiyin Li ◽  
Yan Wu
Keyword(s):  
Power Series ◽  
Probability Space ◽  
Random Variables ◽  
Random Power Series ◽  
Independent Identically Distributed

Aulaskari et al. proved if 0 < p < 1 and ε n is sequence of independent, identically distributed Rademacher random variables on a probability space, then the condition Σ n = 0 ∞ n 1 − p a n 2 < ∞ implies that the random power series R f z = ∑ n = 0 ∞ a n ε n z n ∈ Q p almost surely. In this paper, we improve this result showing that the condition Σ n = 0 ∞ n 1 − p a n 2 < ∞ actually implies R f ∈ Q p , 0 almost surely.

scholarly journals On Inhomogeneous Bernoulli Convolutions and Random Power Series

2011 ◽  
Vol 36 (1) ◽  
pp. 213 ◽  
Author(s):  
Antonios Bisbas ◽  
Jörg Neunhäuserer
Keyword(s):  
Power Series ◽  
Random Power Series ◽  
Bernoulli Convolutions

scholarly journals Divergence of random power series.

1959 ◽  
Vol 6 (4) ◽  
pp. 343-347 ◽  
Author(s):  
A. Dvoretzky ◽  
P. Erdős
Keyword(s):  
Power Series ◽  
Random Power Series

The distribution of the values of a random power series in the unit disk

1983 ◽  
Vol 94 (3-4) ◽  
pp. 251-263 ◽  
Author(s):  
Matthias Jakob ◽  
A. C. Offord
Keyword(s):  
Power Series ◽  
Unit Disk ◽  
Random Variables ◽  
Equal Probability ◽  
Independent Random Variables ◽  
Random Power Series ◽  
The Family ◽  
Unit Radius ◽  
Image Position ◽  
Almost All

SynopsisThis is a study of the family of power series where Σ αnZn has unit radius of convergence and the εn are independent random variables taking the values ±1 with equal probability. It is shown that ifthen almost all these power series take every complex value infinitely often in the unit disk.

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