Approximating martingales and the central limit theorem for strictly stationary processes
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Publication:1208930
DOI10.1016/0304-4149(93)90037-5zbMath0765.60025OpenAlexW2117970368MaRDI QIDQ1208930
Publication date: 16 May 1993
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0304-4149(93)90037-5
central limit theoremsmeasure preserving transformationmartingale differencestationary linear processes
Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Measure-preserving transformations (28D05) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)
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Cites Work
- On moment conditions for normed sums of independent variables and martingale differences
- Martingale convergence to mixtures of infinitely divisible laws
- On non-ergodic versions of limit theorems
- On the central limit theorem for stationary processes
- Über unbedingte Konvergenz in Funktionenraümen (I)
- On the central limit theorem and iterated logarithm law for stationary processes
- The Lindeberg-Levy Theorem for Martingales
- LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS
- A Central Limit Theorem for a Class of Dependent Random Variables
- Ergodic sets
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