On the exactness of the Wu-Woodroofe approximation

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the exactness of the Wu-Woodroofe approximation

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

On the exactness of the Wu-Woodroofe approximation

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

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Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

Stochastic Processes and their Applications

ISSN

0304-4149

e-ISSN

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Svazek periodika

119

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

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Kód UT WoS článku

000266744500003

EID výsledku v databázi Scopus

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