Rates of clustering in Strassen's LIL for partial sum processes

DOI10.1007/BF01192960zbMath0792.60029MaRDI QIDQ1326260

Uwe Einmahl, David M. Mason

Publication date: 6 June 1994

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

zbMATH Keywords

Wiener processstrong approximationfunctional law of the iterated logarithmrate of clustering

Mathematics Subject Classification ID

Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (8)

Clustering behavior of finite variance partial sum processes ⋮ Some remarks on a question of Strassen ⋮ LIL for the Adjusted Range of Partial Sums in AR(1) Models with Possibly Infinite Variance ⋮ Rates of clustering in FLIL for weighted partial sum processes ⋮ A new strong invariance principle for sums of independent random vectors ⋮ Rate of strong Gaussian approximation for sums of i.i.d. multidimensional random vectors ⋮ A generalization of strassen's functional LIL ⋮ The accuracy of strong Gaussian approximation for sums of independent random vectors

Cites Work

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• A lim inf result in Strassen's law of the iterated logarithm
• Rates of clustering in Strassen's LIL for Brownian motion
• On the rate of convergence in Strassen's law of the iterated logarithm
• Strong invariance principles for partial sums of independent random vectors
• Rates of convergence for the functional LIL
• Exact rate of convergence in Strassen's law of the iterated logarithm
• On the speed of convergence in Strassen's law of the iterated logarithm
• Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm
• A relation between Chung's and Strassen's laws of the iterated logarithm
• An invariance principle for the law of the iterated logarithm

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