A bounded law of the iterated logarithm for Hilbert space valued martingales and its application to U-statistics

DOI10.1007/BF00343899zbMath0572.60012MaRDI QIDQ1062339

Walter Philipp, Manfred Denker, Herold G. Dehling

Publication date: 1986

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

zbMATH Keywords

Hilbert spaceinvariance principlesU-statisticslaw of the iterated logarithm for martingales

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (12)

The LIL for canonical \(U\)-statistics of order 2 ⋮ \(U\)-statistics in Banach spaces ⋮ Some dimension-free features of vector-valued martingales ⋮ On the law of the iterated logarithm for canonical \(U\)-statistics and processes ⋮ The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals ⋮ Limit distributions of V- and U-statistics in terms of multiple stochastic Wiener-type integrals ⋮ Some laws of the iterated logarithm in Hilbertian autoregressive models ⋮ Rates of convergence in the strong law of large numbers for degenerate U- statistics ⋮ Law of the iterated logarithm for U-statistics ⋮ A compact law of the iterated logarithm for UH-statistics ⋮ Nonparametric Sequential Comparison of Two Treatments with Random Allocation ⋮ A compact LIL for martingales in \(2\)-smooth Banach spaces with applications

Cites Work

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• A note on invariance principles for v. Mises' statistics
• The functional law of the iterated logarithm for von Mises functionals and multiple Wiener integrals
• Some results on the LIL in Banach space with applications to weighted empirical processes
• Invariance principles for von Mises and U-statistics
• On the limit theorems for random variables with values in the spaces L p (2?p<?)
• An almost sure Invariance Principle for Hilbert Space Valued Martingales
• Mises’ Theorem on the Asymptotic Behavior of Functionals of Empirical Distribution Functions and Its Statistical Applications

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