Uniform large and moderate deviations for functional empirical processes

DOI10.1016/S0304-4149(97)00006-9zbMath0890.60022OpenAlexW2068917233MaRDI QIDQ1382536

Amir Dembo, Tim Zajic

Publication date: 29 March 1998

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(97)00006-9

zbMATH Keywords

large deviationsempirical processmoderate deviationslaw of iterated logarithm integrability

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

Moderate deviation principles for trajectories of sums of independent Banach space valued random variables ⋮ Sample path moderate deviations for the cumulative fluid produced by an increasing number of exponential on-off sources ⋮ Estimation of the realized (co-)volatility vector: large deviations approach ⋮ The law of the iterated logarithm for two-dimensional stochastic Navier-Stokes equations ⋮ Moderate deviations and functional LIL for super-Brownian motion ⋮ Large deviation properties of constant rate data streams sharing a buffer with long-range dependent traffic in critical loading ⋮ Moderate deviation principles for stochastic differential equations with jumps ⋮ Sample path large deviations for multiclass feedforward queueing networks in critical loading ⋮ Sample path moderate deviations for a family of long-range dependent traffic and associated queue length processes ⋮ The law of the iterated logarithm for a class of SPDEs ⋮ Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem ⋮ Exponential bounds for the probability deviations of sums of random fields ⋮ Moderate deviations for randomly perturbed dynamical systems ⋮ Moderate deviations for martingale differences and applications to φ -mixing sequences

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large deviations and stochastic homogenization
• Functional laws of the iterated logarithm for the partial sums of i.i.d. random variables in the asymmetric stable law
• Large deviations, moderate deviations and LIL for empirical processes
• Sharper bounds for Gaussian and empirical processes
• Comparison theorems, random geometry and some limit theorems for empirical processes
• A function space large deviation principle for certain stochastic integrals
• Large deviations: From empirical mean and measure to partial sums process
• Large Deviations for Trajectories of Multi-Dimensional Random Walks