On discrete time extremal processes
- 1 September 1974
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 6 (3) , 580-592
- https://doi.org/10.2307/1426235
Abstract
Upper record values and times and inter-record times are studied in their rôles as embedded structures in discrete time extremal processes. Various continuous time approximations to the discrete-time processes are analysed, especially as processes over their state spaces. Discrete time processes, suitably normalized after crossing a threshold T, are shown to converge to limiting continuous time processes as T → ∞ under suitable assumptions on the underlying CDF F, for example, when 1 — F varies regularly at ∞, and more generally. Discrete time extremal processes viewed as processes over their state spaces are noted to have an interesting interpretation in terms of processes of population growth.Keywords
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