Extreme-value asymptotics for affine random walks (Q386672)

The paper deals with the asymptotic behavior of a certain sequence of point processes associated to an \textit{affine random walk} \((X_n)\) defined on the Euclidian space \(\mathbb{R}^d\). More precisely, this sequence is related to the extreme values of the considered random walk. Under some specific multivariate regular variation conditions, the authors prove the convergence in distribution of the sequence of point processes. The limit law is expressed in terms of a homogeneous measure on \(\mathbb{R}^d\setminus\{0\}\). In particular, it is shown that the normalized extreme values of the random walk \(\left(\left|X_n\right|\right)\) follow a Fréchet law.NEWLINENEWLINEThis study is mainly based on the theory of regularly varying multivariate time series that was developed by \textit{B. Basrak} and \textit{J. Segers} [Stochastic Processes Appl. 119, No. 4, 1055--1080 (2009; Zbl 1161.60319); erratum ibid. 121, No. 4, 896--898 (2011)].