Multivariate Regular Variation and its Applications

Dioulde Habibatou Mariko
In this thesis, we review the basic notions related to univariate regular variation and study some fundamental properties of regularly varying random variables. We then consider the notion of regular variation in the multivariate case. After collecting some results from multivariate regular variation for random vectors with values in $\mathbb{R}_{+}^{d}$, we discuss its properties and examine several examples of multivariate regularly varying random vectors such as independent and identically distributed random vectors, fully dependent random...
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