Subexponential Distributions

Specialeforsvar ved Michael Skibsted

Titel: Subexponential Distributions

Abstract: The idea of this thesis is to review some of the literature on the classical theory of univariate subexponentiality and some of the more recent notions - ”and associated theory - ”of multivariate subexponentiality, respectively. Subexponential distributions are characterized by the principle of a single big jump and include a much larger variety of distributions than the regularly varying class. We will be interested in the definitions and associated theory of multivariate subexponentiality provided by Omey [25]. This notion of multivariate subexponentiality is a natural extension of the univariate case. We start by reviewing univariate subexponentiality and continue by introducing the tractable notions of multivariate subexponentiality proposed in Omey [25], showing several multivariate analogs of important - previously shown - ”univariate results. Finally, we expose a serious weakness governing Omey's first multivariate notion 

Vejleder: Thomas Mikosch
Censor:   Søren Asmussen, Aarhus Universitet