Titlebook: High Dimensional Probability III; Jørgen Hoffmann-Jørgensen,Jon A. Wellner,Michael B Conference proceedings 2003 Springer Science+Business

Flustered

Rates of Convergence for Lévy’s Modulus of Continuity and Hinchin’s Law of the Iterated LogarithmFor a standard Wiener process ., denoting . and ., we have proved the following two results: . converges down to 1 at least as fast as . and . converges down to 1 at least as fast as .

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On the Limit Set in the Law of the Iterated Logarithm for ,-statistics of Order TwoWe find the cluster set in the Law of the Iterated Logarithm for U-statistics of order 2 in some interesting special cases. The lim sup is an unusual function of the quantities that determine the Bounded LIL.

FEIGN

Perturbation Approach Applied to the Asymptotic Study of Random OperatorsWe prove that, for the main kind of limit theorems (laws of large numbers, central limit theorems, large deviations principles, laws of the iterated logarithm) asymptotic results for selfadjoint random operators yield equivalent results for their eigenvalues and associated projections.

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LAPSE

Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their ApplicationWe consider strong limit theorems such as bounded and compact laws of the iterated logarithm and an almost sure invariance principle for mixing random variables with values in Hilbert space. Applying these results we prove an almost sure invariance principle for U-statistics as well.