On the central limit theorem for some birth and death processes

Tymoteusz Chojecki. "On the central limit theorem for some birth and death processes." Annales UMCS, Mathematica 65.1 (2011): 21-31. <http://eudml.org/doc/267629>.

@article{TymoteuszChojecki2011,
abstract = {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.},
author = {Tymoteusz Chojecki},
journal = {Annales UMCS, Mathematica},
keywords = {Central limit theorem; Markov chain; Lamperti's problem; birth and death processes; Kipnis-Varadhan theory; spectral gap; central limit theorem},
language = {eng},
number = {1},
pages = {21-31},
title = {On the central limit theorem for some birth and death processes},
url = {http://eudml.org/doc/267629},
volume = {65},
year = {2011},
}

TY - JOUR
AU - Tymoteusz Chojecki
TI - On the central limit theorem for some birth and death processes
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 1
SP - 21
EP - 31
AB - 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.
LA - eng
KW - Central limit theorem; Markov chain; Lamperti's problem; birth and death processes; Kipnis-Varadhan theory; spectral gap; central limit theorem
UR - http://eudml.org/doc/267629
ER -