Two extreme value processes arising in hydrology

1 March 1976

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 13 (1) , 190-194
https://doi.org/10.2307/3212683

Abstract

Let T_n be the time of occurrence of the nth flood peak in a hydrological system and X_n the amount by which the peak exceeds a base level. We assume that ((T_n, X_n)) is a Poisson random measure with mean measure μ(dx) K(x, dy). In this note we characterize two extreme value processes which are functionals of ((T_n, X_n)). The set-parameterized process {M_A} defined by M_A = sup {X_n:T_n ∈ A} is additive and we compute its one-dimensional distributions explicitly. The process (M_t), where M_t = sup{X_n: T_n ≦ t}, is a non-homogeneous strong Markov process. Our results extend but computationally simplify those of previous models.

Keywords

This publication has 1 reference indexed in Scilit:

On Some Problems Involving Random Number of Random Variables
The Annals of Mathematical Statistics, 1970