Displaying similar documents to “Exponential inequalities and functional central limit theorems for random fields”

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2001)

ESAIM: Probability and Statistics

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We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform φ -mixing random fields, we require both finite fourth moments and an algebraic decay of the...

Prediction problems

Nguyen Van Thu

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CONTENTSIntroduction......................................................................................................................................... 5I. Prediction of strictly stationary random fields.................................................................................... 6II. Prediction of stationary-in-norm fields in Banach spaces of random variables........................ 23 § 1. Banach spaces of random variables...................................................................................

An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law

Hartmut Lanzinger (2010)

ESAIM: Probability and Statistics

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We prove a strong law of large numbers for moving averages of independent, identically distributed random variables with certain subexponential distributions. These random variables show a behavior that can be considered intermediate between the classical strong law and the Erdös-Rényi law. We further show that the difference from the classical behavior is due to the influence of extreme terms.