Given a finite alphabet, there is an inductive method for constructing a stationary measure on doubly infinite words from this alphabet. This construction can be randomized; the main focus here is on a particular uniform randomization which intuitively corresponds to the idea of choosing a generic stationary process. It is shown that with probability 1, the random stationary process has zero entropy and gives positive probability to every periodic infinite word.
Publié le : 1992-07-14
Classification:
Stationary process,
entropy,
random measure,
60G10,
28D05,
60G57
@article{1176989685,
author = {Alexander, Kenneth S. and Kalikow, Steven A.},
title = {Random Stationary Processes},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 1174-1198},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989685}
}
Alexander, Kenneth S.; Kalikow, Steven A. Random Stationary Processes. Ann. Probab., Tome 20 (1992) no. 4, pp. 1174-1198. http://gdmltest.u-ga.fr/item/1176989685/