Natural boundary of the random power series

We investigate convergence properties of random Taylor series whose coefficients are ψ -mixing random variables. In particular, we give sufficient conditions such that the circle of the convergence of the series forms almost surely a natural boundary.

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Bibliographic Details
Published inScience China. Mathematics Vol. 65; no. 5; pp. 951 - 970
Main Authors Huo, Yingying, Sun, Daochun, Yang, Xiaochuan, Fang, Lulu
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.05.2022
Springer Nature B.V
Subjects
Applications of Mathematics
Convergence
Mathematics
Mathematics and Statistics
Power series
Random variables
Taylor series
30D20
natural boundary
random power series
60F99
mixing
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Summary:We investigate convergence properties of random Taylor series whose coefficients are ψ -mixing random variables. In particular, we give sufficient conditions such that the circle of the convergence of the series forms almost surely a natural boundary.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-019-1765-1