Logarithmic asymptotics for the supremum of a stochastic process

DOI10.1214/aoap/1050689587zbMath1032.60025OpenAlexW2016807471MaRDI QIDQ1413673

Wayne G. Sullivan, John T. Lewis, Ken R. Duffy

Publication date: 17 November 2003

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1050689587

zbMATH Keywords

large deviation principletail asymptotics

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Large deviations (60F10)

Related Items (14)

The Large Deviations of Estimating Rate Functions ⋮ Large Deviations for a Damped Telegraph Process ⋮ Estimating Loynes' exponent ⋮ Steady-state GI/G/\(n\) queue in the Halfin-Whitt regime ⋮ Asymptotic results for the last zero crossing time of a Brownian motion with non-null drift ⋮ Power estimates for ruin probabilities ⋮ Large deviation results on some estimators for stationary Gaussian processes ⋮ On the asymptotic behavior of the hyperbolic Brownian motion ⋮ Tail asymptotics for discrete event systems ⋮ Tail Asymptotics for Monotone-Separable Networks ⋮ Logarithmic asymptotics for a single-server processing distinguishable sources ⋮ Tail asymptotics for busy periods ⋮ Large deviations of bivariate Gaussian extrema ⋮ Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings

Cites Work

• Large deviations for a general class of random vectors
• Large deviations of heavy-tailed sums with applications in insurance
• On Large Deviations from the Invariant Measure
• Asymptotic behavior of a multiplexer fed by a long-range dependent process
• Large deviations and overflow probabilities for the general single-server queue, with applications
• Large buffer asymptotics for the queue with fractional Brownian input
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