# Subnormal independent random variables and Levy’s phenomenon for entire functions

Author
Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract
Suppose that $(Z_n)$ is a sequence of real independent subnormal random variables, i.e. such that there exists $D>0$ satisfying following inequality for expectation $\mathbf{E}(e^{\lambda_0Z_k})\leq e ^{D \lambda_0^2}$ for any $k\in\mathbb{N}$ for all $\lambda_0\in\mathbb{R}$. In this paper is proved that for random entire functions of the form $f(z,\omega)=\sum_{n=0}^{+\infty}Z_n(\omega)a_nz^n$ Levy's phenomenon holds.
Keywords
entire function; Levy’s phenomenon; subnormal random variables
DOI
doi:10.15330/ms.47.1.10-19
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Pages
10-19
Volume
47
Issue
1
Year
2017
Journal
Matematychni Studii
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