Uniform renewal theory with applications to expansions of random geometric sums

DOI10.1239/aap/1198177240zbMath1132.60060OpenAlexW2126545263MaRDI QIDQ5443152

Peter W. Glynn, Jose H. Blanchet

Publication date: 20 February 2008

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1198177240

zbMATH Keywords

renewal theorycorrected diffusion approximationrandom geometric sum

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Traffic problems in operations research (90B20) Renewal theory (60K05)

Related Items (13)

Trigonometric series and self-similar sets ⋮ Finitary isomorphisms of renewal point processes and continuous-time regenerative processes ⋮ Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics ⋮ Asymptotic expansions of defective renewal equations with applications to perturbed risk models and processor sharing queues ⋮ Dispersion models for geometric sums ⋮ Unnamed Item ⋮ Connecting Renewal Age Processes with M/D/1 and M/D/∞ Queues Through Stick Breaking ⋮ On the transition from heavy traffic to heavy tails for the \(M/G/1\) queue: the regularly varying case ⋮ Compensating for Dynamic Supply Disruptions: Backup Flexibility Design ⋮ Uniform approximations for the \(M/G/1\) queue with subexponential processing times ⋮ Unnamed Item ⋮ Higher-order expansions for compound distributions and ruin probabilities with subexponential claims ⋮ AN EXTENSION OF RANDOM SUMMATIONS OF INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES

Cites Work

• Unnamed Item
• Sequential analysis. Tests and confidence intervals
• Probability approximations via the Poisson clumping heuristic
• Markov chain models - rarity and exponentiality
• Ladder heights, Gaussian random walks and the Riemann zeta function
• Remainder term estimates of the renewal function
• Uniform Markov renewal theory and ruin probabilities in Markov random walks.
• Tauberian remainder theorems
• Estimates for Overshooting an Arbitrary Boundary by a Random Walk and Their Applications
• Approximations for the probability of ruin within finite time
• Comment on ‘Corrected diffusion approximations in certain random walk problems'
• Corrected diffusion approximations in certain random walk problems
• Applied Probability and Queues
• Exponential Approximations for Tail Probabilities in Queues, I: Waiting Times
• On Moment Generating Functions and Renewal Theory
• Probability

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