Ergodicity and central limit theorems for a class of Markov processes

Rabi N. Bhattacharya and Oesook Lee

Journal of Multivariate Analysis, 1988, vol. 27, issue 1, 80-90

Abstract: 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 [8] 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.

Keywords: contractions; invariant; distribution; functional; central; limit; theorem (search for similar items in EconPapers)
Date: 1988
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