Fluctuation theory in continuous time
- 1 September 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 7 (04) , 705-766
- https://doi.org/10.1017/s0001867800040982
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.Keywords
This publication has 63 references indexed in Scilit:
- Exit problem for a spectrally positive processAdvances in Applied Probability, 1973
- A note on random walks. IIJournal of Applied Probability, 1973
- The distribution of the content of finite damsJournal of Applied Probability, 1967
- The Distribution of the Time the Maximum is Achieved for Processes with Independent IncrementsTheory of Probability and Its Applications, 1966
- On the Distribution of the Maximum of a Process with Independent IncrementsTheory of Probability and Its Applications, 1965
- On a necessary and sufficient condition that an infinitely divisible distribution be absolutely continuousTransactions of the American Mathematical Society, 1965
- On the distribution of the supremum for stochastic processes with interchangeable incrementsTransactions of the American Mathematical Society, 1965
- A storage model with continuous infinitely divisible inputsMathematical Proceedings of the Cambridge Philosophical Society, 1963
- Limit Theorems for Stochastic Processes with Independent IncrementsTheory of Probability and Its Applications, 1957
- Investigation of waiting time problems by reduction to Markov processesActa Mathematica Hungarica, 1955