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On the Central Limit Theorem for Geometrically Ergodic Markov Chains

Olle Häggström (Institutionen för matematiska vetenskaper, matematisk statistik)
Probability theory and related fields (0178-8051). Vol. 132 (2005), 1, p. 74-82.
[Artikel, refereegranskad vetenskaplig]

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.

Denna post skapades 2006-12-21. Senast ändrad 2013-06-10.
CPL Pubid: 24484


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Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)



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