We prove that a Gaussian Taylor series takes almost surely every complex value with at most one exception. This presents an answer to a problem of Kahane. We also present an example to show some differences between Gaussian and classical Taylor series.
Publié le : 1987-07-14
Classification:
Recurrence and transience property,
Gaussian Taylor series,
boundary behaviour,
60G15,
60G50
@article{1176992091,
author = {Hwang, J. S.},
title = {On a Problem of Kahane About the Image of Gaussian Taylor Series},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 1203-1209},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992091}
}
Hwang, J. S. On a Problem of Kahane About the Image of Gaussian Taylor Series. Ann. Probab., Tome 15 (1987) no. 4, pp. 1203-1209. http://gdmltest.u-ga.fr/item/1176992091/