A new strong invariance principle for sums of independent random vectors
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Publication:2452916
DOI10.1007/s10958-009-9676-8zbMath1288.60040OpenAlexW2021789623MaRDI QIDQ2452916
Publication date: 6 June 2014
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10958-009-9676-8
Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)
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Cites Work
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- A useful estimate in the multidimensional invariance principle
- Strong invariance principles for partial sums of independent random vectors
- Extensions of results of Komlós, Major, and Tusnády to the multivariate case
- An improvement of Strassen's invariance principle
- Rates of clustering in Strassen's LIL for partial sum processes
- A generalization of strassen's functional LIL
- Some results on two-sided LIL behavior
- Characterization of LIL behavior in Banach space
- An approximation of partial sums of independent RV's, and the sample DF. II
- The approximation of partial sums of independent RV's
- Multidimensional version of the results of Komlos, Major and Tusnady for vectors with finite exponential moments
- An invariance principle for the law of the iterated logarithm
