The Annals of Probability

Explicit Construction of Invariant Measures for a Class of Continuous State Markov Processes

S. Halfin

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Abstract

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.

Article information

Source
Ann. Probab., Volume 3, Number 5 (1975), 859-864.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996272

Digital Object Identifier
doi:10.1214/aop/1176996272

Mathematical Reviews number (MathSciNet)
MR386019

Zentralblatt MATH identifier
0341.60037

JSTOR
links.jstor.org

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 10K05 10K10

Keywords
Continuous state Markov processes $\beta$-expansions invariant measures Saltus functions

Citation

Halfin, S. Explicit Construction of Invariant Measures for a Class of Continuous State Markov Processes. Ann. Probab. 3 (1975), no. 5, 859--864. doi:10.1214/aop/1176996272. https://projecteuclid.org/euclid.aop/1176996272


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