Inverses of extremal processes
- 1 June 1974
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 6 (2) , 392-406
- https://doi.org/10.2307/1426300
Abstract
The inverse of an extremal process {Y(t),t≧ 0} is an additive process whose Lévy measure can be computed. This measure controls among other things the Poisson number of jumps ofYwhileYis in the vertical window (c, d]. A simple transformation of the inverse of the extremal process governed by Λ (x) = exp{–e–x} is also extremal-Λ (x) and this fact enables one to relate behavior ofY-Λ att= ∞ to behavior neart= 0. Some extensions of these ideas to sample sequences of maxima of i.i.d. random variables are carried out.Keywords
This publication has 9 references indexed in Scilit:
- The structure of extremal processesAdvances in Applied Probability, 1973
- Almost sure limit points of record valuesJournal of Applied Probability, 1973
- Extremal processes and record value timesJournal of Applied Probability, 1973
- Record values and inter-record timesJournal of Applied Probability, 1973
- The Rate of Growth of Sample MaximaThe Annals of Mathematical Statistics, 1972
- On record values and record timesJournal of Applied Probability, 1972
- Extremal Processes, IIIllinois Journal of Mathematics, 1966
- Extremal ProcessesThe Annals of Mathematical Statistics, 1964
- On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.MATHEMATICA SCANDINAVICA, 1961