On the Central Limit Theorem for Geometrically Ergodic Markov Chains
Artikel i vetenskaplig tidskrift, 2005

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)) 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.


Olle Häggström

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Probability Theory and Related Fields

0178-8051 (ISSN) 1432-2064 (eISSN)

Vol. 132 74-82