Details

Autor(en) / Beteiligte

• HÄGGSTRÖM, Olle

Titel

On the central limit theorem for geometrically ergodic Markov chains

Ist Teil von

• Probability theory and related fields, 2005-05, Vol.132 (1), p.74-82

Ort / Verlag

Heidelberg: Springer

Erscheinungsjahr

2005

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• Let X0,X1,... be a geometrically ergodic Markov chain with state space [chi] and stationary distribution [phi]. It is known that if h:[chi][arrow pointing right] R satisfies [phi] ([absolute value of] h [squared]+^super [epsilon]) [is less than] [infinity] for some [epsilon] is greater than 0, then the normalized sums of the X^sub i^'s obey a central limit theorem. Here we show, by means of a counterexample, that the condition [phi] ([absolute value of] h [squared]+^super [epsilon]) [is less than] [infinity], then the normalized sums of the X^sub i^'s obey a central limit theorem. Here we show, by means of a counterexample, that the condition [phi] ([absolute value of] h [squared]+^super [epsilon]) cannot be weakened to only assuming a finite second moment, i.e. [phi](h)[squared] [is less than] [infinity].