TY - JOUR
T1 - Ergodicity and central limit theorems for a class of Markov processes
AU - Bhattacharya, Rabi N.
AU - Lee, Oesook
N1 - Funding Information:
supported by NSF Grant DMS 8503358.
PY - 1988/10
Y1 - 1988/10
N2 - 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.
AB - 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.
KW - contractions
KW - functional central limit theorem
KW - invariant distribution
UR - http://www.scopus.com/inward/record.url?scp=38249029227&partnerID=8YFLogxK
U2 - 10.1016/0047-259X(88)90117-0
DO - 10.1016/0047-259X(88)90117-0
M3 - Article
AN - SCOPUS:38249029227
SN - 0047-259X
VL - 27
SP - 80
EP - 90
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 1
ER -