(G, λ)-Extremal Processes and Their Relationship with Max-Stable Processes
(G, λ)-Extremal Processes and Their Relationship with Max-Stable Processes
2000 Mathematics Subject Classification: 60G70, 60G18. 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. This paper is partially supported by NFSI-Bulgaria, Grant No VU-MI-105/2005.
- Institute of Mathematics and Informatics Bulgaria
- Bulgarian Academy of Sciences Bulgaria
G-extremal processes, self-similar processes, max-stable processes
G-extremal processes, self-similar processes, max-stable processes
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