Fluctuation theory in continuous time

Ν. H. Bingham

179 citations0/0 files storedAdvances in Applied Probability

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Probability and Risk Models Stochastic processes and statistical mechanics Advanced Queuing Theory Analysis

Abstract

Our aim here is to give a survey of that part of continuous-time fluctuation theory which can be approached in terms of functionals of Lévy processes, our principal tools being Wiener-Hopf factorisation and local-time theory. Particular emphasis is given to one- and two-sided exit problems for spectrally negative and spectrally positive processes, and their applications to queues and dams. In addition, we give some weak-convergence theorems of heavy-traffic type, and some tail-estimates involving regular variation.

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References

1951Some Problems in the Theory of Queues 1961The single server queue in heavy traffic 1970Multiple channel queues in heavy traffic. I 1983The Single Server Queue.1955Investigation of waiting time problems by reduction to Markov processes 1966On the algebra of queues 1957On Queues with Poisson Arrivals 1964General Stochastic Processes in the Theory of Queues

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