On the central limit theorem for geometrically ergodic Markov chains
成果类型：
Article
署名作者：
Häggström, O
署名单位：
Chalmers University of Technology
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-004-0390-7
发表日期：
2005
页码：
74-82
关键词：
摘要：
Let X-0,X-1,... be a geometrically ergodic Markov chain with state space X and stationary distribution pi. It is known that if h:X -> R satisfies pi(vertical bar h vertical bar(2+epsilon)) < infinity for some epsilon > 0, then the normalized sums of the X-i's obey a central limit theorem. Here we show, by means of a counterexample, that the condition pi(vertical bar h vertical bar(2+epsilon)) < infinity cannot be weakened to only assuming a finite second moment, i.e., pi(h(2)) < infinity.
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