Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 18, No 1, (2007), 145p-156p
Abstract:
The study of G-extremal processes was initiated by S. Resnick and M. Rubinovich (1973). Here we transform these processes by a non-decreasing and right-continuous function λ : [0, ∞) → [0, ∞) and investigate relationship between (G; λ)-extremal processes and max-stable processes. We prove that for the processes with independent max-increments if one of the following three statements is given, the other two are equivalent:
a) Y is a max-stable process;
b) Y is a (G; λ)-extremal process;
c) Y is a self-similar extremal process.
