%0 Journal Article
%T On the central limit theorem for some birth and death processes
%A Tymoteusz Chojecki
%J Annales UMCS, Mathematica
%D 2011
%I 
%R 10.2478/v10062-011-0003-8
%X Suppose that {Xn, n ¡Ý 0} is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem converge in law to a normal random variable, as N ¡ú +¡Þ. For a stationary Markov chain with the L2 spectral gap the theorem holds for all V such that V (X0) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables V for which the CLT holds for a class of birth and death chains whose dynamics has no spectral gap, so that Gordin's result cannot be used and the result follows from an application of Kipnis-Varadhan theory.
%K Central limit theorem
%K Markov chain
%K Lamperti's problem
%K birth and death processes
%K Kipnis-Varadhan theory
%K spectral gap
%U http://versita.metapress.com/content/lt50106v90g576q7/?p=f056d4531dea4dd28d60f971568ab259&pi=2