On the exactness of the Wu-Woodroofe approximation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F09%3A00011047" target="_blank" >RIV/60076658:12510/09:00011047 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On the exactness of the Wu-Woodroofe approximation

Original language description

Let (Xi) be a stationary process adapted to a filtration View the MathML source, E(Xi)=0, View the MathML source; by View the MathML source we denote the partial sums and View the MathML source. Wu and Woodroofe [Wei Biao Wu, M. Woodroofe, Martingale approximation for sums of stationary processes, Ann. Probab. 32 (2004) 1674?1690] have shown that if View the MathML source then there exists an array of row-wise stationary martingale difference sequences approximating the partial sums Sn. If View the MathML source then by [M. Maxwell, M. Woodroofe, Central limit theorems for additive functionals of Markov chains, Ann. Probab. 28 (2000) 713?724] there exists a stationary martingale difference sequence approximating the partial sums Sn, and the central limit theorem holds. We will show that the process (Xi) can be found so that View the MathML source, View the MathML source constant but the central limit theorem does not hold. The linear growth of the variances View the MathML source is a

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BB - Applied statistics, operational research

OECD FORD branch

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Project

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Continuities

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Stochastic Processes and their Applications

ISSN

0304-4149

e-ISSN

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Volume of the periodical

119

Issue of the periodical within the volume

7

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

8

Pages from-to

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UT code for WoS article

000266744500003

EID of the result in the Scopus database

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