# On the central limit theorem for some birth and death processes

Annales UMCS, Mathematica (2011)

- Volume: 65, Issue: 1, page 21-31
- ISSN: 2083-7402

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topTymoteusz 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 -

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