The supremum distribution of a Lévy process with no negative jumps
- 1 June 1977
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 9 (2), 417-422
- https://doi.org/10.2307/1426392
Abstract
Let be a process with stationary, independent increments and no negative jumps. Let be this same process modified by a reflecting barrier at zero (a storage process). Assuming that – and denote by ψ(s) the exponent function of X. A simple formula is derived for the Laplace transform of as a function of W(0). Using the fact that the distribution of M is the unique stationary distribution of the Markov process W, this yields an elementary proof that the Laplace transform of M is µs/ψ(s). If it follows that These surprisingly simple formulas were originally obtained by Zolotarev using analytical methods.Keywords
This publication has 3 references indexed in Scilit:
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- The First Passage Time of a Level and the Behavior at Infinity for a Class of Processes with Independent IncrementsTheory of Probability and Its Applications, 1964