We consider a class of discrete parameter Markov processes on a complete separable metric space S arising from successive compositions of i.i.d. random maps on S into itself, the compositions becoming contractions eventually. A sufficient condition for ergodicity is found, extending a result of Dubins and Freedman  for compact S. By identifying a broad subset of the range of the generator, a functional central limit theorem is proved for arbitrary Lipschitzian functions on S, without requiring any mixing type condition or irreducibility.
- functional central limit theorem
- invariant distribution
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty