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On the norming constants occuring in convergent Markov chains
Published online by Cambridge University Press: 17 April 2009
Extract
Several theorems concerning the norming constants {aṇ} and {bn} making a normed Markov chain {an (Xn+bn): n ≥ 0} convergent in distribution (or in probability) are given. It is shown that if Rényi's mixing conditions holds, and
, whereas in the general case
with α ≠ 0 and
exists and are finite. Examples regarding maxima of independent and identically distributed random variables, random walk, and branching processes are considered.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 17 , Issue 2 , October 1977 , pp. 193 - 205
- Copyright
- Copyright © Australian Mathematical Society 1977
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