Moderate deviation principles for trajectories of sums of independent Banach space valued random variables

DOI10.1090/S0002-9947-01-02893-8zbMath1049.60023OpenAlexW1574210422MaRDI QIDQ4806470

Tzong-Yow Lee, Hu, Yijun

Publication date: 14 May 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02893-8

zbMATH Keywords

Banach spacecentral limit theoremrate functionlaw of iterated logarithmmoderate deviation principle

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Functional limit theorems; invariance principles (60F17)

Related Items (5)

Moderate deviation principles for the trajectories of inhomogeneous random walks ⋮ Extremes of weighted Brownian bridges in increasing dimension ⋮ Moderate deviations for stationary sequences of Hilbert-valued bounded random variables ⋮ Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth ⋮ Sample path moderate deviations for a family of long-range dependent traffic and associated queue length processes

Cites Work

• Some results on the LIL in Banach space with applications to weighted empirical processes
• Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi. (On moderate deviations of sums of independent and identically distributed vector valued random variables)
• Moderate deviations for empirical measures of Markov chains: Upper bounds
• Large deviations for trajectories of sums of independent random variables
• Large deviations for vector-valued Lévy processes
• Moderate deviations for empirical measures of Markov chains: Lower bounds
• Uniform large and moderate deviations for functional empirical processes
• Large deviations: From empirical mean and measure to partial sums process
• Upper bounds for large deviations of dependent random vectors
• Moderate Deviations and Associated Laplace Approximations for Sums of Independent Random Vectors
• The Large Deviation Principle for Stochastic Processes. Part I
• Asymptotic probabilities and differential equations
• Large deviations for processes with independent increments
• Laplace approximations for sums of independent random vectors
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