Filtern
Volltext vorhanden
- ja (1)
Gehört zur Bibliographie
- ja (1)
Erscheinungsjahr
- 2016 (1) (entfernen)
Dokumenttyp
- Dissertation (1)
Sprache
- Englisch (1) (entfernen)
Schlagworte
- Rekord (1) (entfernen)
Institut
Extreme value theory is concerned with the stochastic modeling of rare and extreme events. While fundamental theories of classical stochastics - such as the laws of small numbers or the central limit theorem - are used to investigate the asymptotic behavior of the sum of random variables, extreme value theory focuses on the maximum or minimum of a set of observations. The limit distribution of the normalized sample maximum among a sequence of independent and identically distributed random variables can be characterized by means of so-called max-stable distributions.
This dissertation concerns with different aspects of the theory of max-stable random vectors and stochastic processes. In particular, the concept of 'differentiability in distribution' of a max-stable process is introduced and investigated. Moreover, 'generalized max-linear models' are introduced in order to interpolate a known max-stable random vector by a max-stable process. Further, the connection between extreme value theory and multivariate records is established. In particular, so-called 'complete' and 'simple' records are introduced as well as it is examined their asymptotic behavior.