A generalization of strassen's functional LIL

DOI10.1007/s10959-007-0091-0zbMath1140.60015arXivmath/0601613OpenAlexW2066236428MaRDI QIDQ2471131

Uwe Einmahl

Publication date: 18 February 2008

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601613

zbMATH Keywords

infinite variancesums of i.i.d. random variablesstrong invariance principle.Hartman--Wintner LILStrassen-type resultsvery slowly varying functions

Mathematics Subject Classification ID

Strong limit theorems (60F15)

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Invariance Principles for Products ofU-Statistics Without Variance, A note on the strong approximation for long memory processes and its application, An almost sure invariance principle for trimmed sums of random vectors, LIL for the Adjusted Range of Partial Sums in AR(1) Models with Possibly Infinite Variance, Strong approximation for \(\rho \)-mixing sequences, A Supplement to the Einmahl–Li Results on Two-Sided Iterated Logarithm Type Behavior for I.I.D. Random Variables, Cluster sets for partial sums and partial sum processes, Characterization of LIL behavior in Banach space, A new strong invariance principle for sums of independent random vectors, A general strong approximation theorem for dependent \(\mathbb R^d\)-valued random vectors, Iterated logarithm type behavior for weighted sums of i.i.d. random variables, On weighted approximations in \(D[0,1\) with applications to self-normalized partial sum processes]

Cites Work

• The LIL when X is in the domain of attraction of a Gaussian law
• Stability results and strong invariance principles for partial sums of Banach space valued random variables
• General one-sided laws of the iterated logarithm
• Toward a general law of the iterated logarithm in Banach space
• Rates of clustering in Strassen's LIL for partial sum processes
• The law of the logarithm for weighted sums of independent random variables
• Strong approximations for partial sums of i.i.d. B-valued r.v.'s in the domain of attraction of a Gaussian law
• On the cluster set problem for the generalized law of the iterated logarithm in Euclidean space
• Some results on two-sided LIL behavior
• A relation between Chung's and Strassen's laws of the iterated logarithm
• Toward a universal law of the iterated logarithm, Part II
• An invariance principle for the law of the iterated logarithm
• The Limit Points of a Normalized Random Walk
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