Martingale approximations for sums of stationary processes.
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Publication:1879842
DOI10.1214/009117904000000351zbMath1057.60022arXivmath/0410160OpenAlexW2065967197MaRDI QIDQ1879842
Wei-Biao Wu, Michael B. Woodroofe
Publication date: 15 September 2004
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0410160
linear processMarkov chaincentral limit theoreminvariance principlemartingalePoisson equationstationary process
Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Functional limit theorems; invariance principles (60F17)
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Cites Work
- A central limit theorem for functions of a Markov chain with applications to shifts
- Limit theorems for functionals of moving averages
- A new weak dependence condition and applications to moment inequalities
- Necessary and sufficient conditions for the conditional central limit theorem
- Central limit theorems for additive functionals of Markov chains.
- Markov chains for exploring posterior distributions. (With discussion)
- On the asymptotic normality of sequences of weak dependent random variables
- Remarks on the functional central limit theorem for martingales
- A central limit theorem for iterated random functions
- Some Limit Theorems for Stationary Processes
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