Applications of Point Process Convergence

Following the theme of this text, in the present chapter \(({\mathbf {X}}_t)_{t\in {\mathbb Z}}\) is an \({\mathbb R}^d\) -valued regularly varying stationary sequence with index \(\alpha >0\) and generic element \(\mathbf {X}\) , and the normalizing sequence \((a_n)\) is chosen such that \(n\,{\mathbb {P}}(|\mathbf {X}|>a_n)\to 1\) a.s. \(n\to \infty \) .