Strong approximations for partial sums of i.i.d. B-valued r.v.'s in the domain of attraction of a Gaussian law

DOI10.1007/BF01848131zbMath0618.60010MaRDI QIDQ1822402

Uwe Einmahl

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

central limit theoremfunctional law of the iterated logarithmstrong invariance principlestrong approximation theorem

Mathematics Subject Classification ID

Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (4)

A Supplement to the Einmahl–Li Results on Two-Sided Iterated Logarithm Type Behavior for I.I.D. Random Variables ⋮ On the limiting behavior of the Pickands estimator for bivariate extreme- value distributions ⋮ A generalization of strassen's functional LIL ⋮ Some results on two-sided LIL behavior

Cites Work

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• Some results on LIL behavior
• The LIL when X is in the domain of attraction of a Gaussian law
• A useful estimate in the multidimensional invariance principle
• Strong invariance principles for partial sums of independent random vectors
• Almost sure invariance principles for partial sums of mixing B-valued random variables
• Some results on the LIL in Banach space with applications to weighted empirical processes
• Approximation theorems for independent and weakly dependent random vectors
• A strong approximation of partial sums of i.i.d. Random variables with infinite variance
• Invariance principles for sums of Banach space valued random elements and empirical processes
• Approximation of partial sums of i.i.d.r.v.s when the summands have only two moments
• Regularly varying functions

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