An explicit construction of invariant measures for a certain class of continuous state Markov processes is presented. A special version of these processes is of interest in the theory of representation of real numbers ($\beta$-expansions). Previous results of Renyi and Parry are generalized, and an open problem of Parry is resolved.
Publié le : 1975-10-14
Classification:
Continuous state Markov processes,
$\beta$-expansions,
invariant measures,
Saltus functions,
60J05,
10K05,
10K10
@article{1176996272,
author = {Halfin, S.},
title = {Explicit Construction of Invariant Measures for a Class of Continuous State Markov Processes},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 859-864},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996272}
}
Halfin, S. Explicit Construction of Invariant Measures for a Class of Continuous State Markov Processes. Ann. Probab., Tome 3 (1975) no. 6, pp. 859-864. http://gdmltest.u-ga.fr/item/1176996272/