Suppose that {Xn, n ≥ 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 (CLT) if [...] [...] converge in law to a normal random variable, as N → +∞. 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.
@article{bwmeta1.element.doi-10_2478_v10062-011-0003-8,
author = {Tymoteusz Chojecki},
title = {On the central limit theorem for some birth and death processes},
journal = {Annales UMCS, Mathematica},
volume = {65},
year = {2011},
pages = {21-31},
zbl = {1247.60104},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-011-0003-8}
}
Tymoteusz Chojecki. On the central limit theorem for some birth and death processes. Annales UMCS, Mathematica, Tome 65 (2011) pp. 21-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-011-0003-8/
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