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.
"Explicit Construction of Invariant Measures for a Class of Continuous State Markov Processes." Ann. Probab. 3 (5) 859 - 864, October, 1975. https://doi.org/10.1214/aop/1176996272