Tillier, C Wintenberger, O

When assessing risks on a finite-time horizon, the problem can often be reduced to the study of a random sequence C(N) = (C 1 ,. .. , C N) of random length N , where C(N) comes from the product of a matrix A(N) of random size N × N and a random sequence X(N) of random length N. Our aim is to build a regular variation framework for such random seque...

Mikosch, Thomas Rezapour, Mohsen Wintenberger, Olivier

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the addi...

Barczy, Mátyás Nedényi, Fanni K. Pap, Gyula
Published in
Lithuanian Mathematical Journal

Abstract. We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton–Watson branching process with regularly varying immigration having index α ∈ (0 , 2). We show that limits of finite-dimensional distributions of appropriately centered and scaled aggregated partial-sum processe...

Torres, Raúl Di Bernardino, Elena Laniado, Henry Lillo, Rosa

In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into the MEVT, giving the opportunity to characterize the recently introduced directional multivariate qua...

Mentemeier, Sebastian Wintenberger, Olivier

We consider multivariate stationary processes $(\boldsymbol{X}_t)$ satisfying a stochastic recurrence equation of the form$$ \boldsymbol{X}_t= \mathbb{ M}_t \boldsymbol{X}_{t-1} + \boldsymbol{Q}_t,$$where $(\boldsymbol{Q}_t)$ are iid random vectors and $$\mathbb{M}_t=\mathrm{Diag}(b_1+c_1 M_t, \dots, b_d+c_d M_t)$$ are iid diagonal matrices and $(M...

Kratz, Marie Prokopenko, Evgeny

We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called 'normex' approach from a univariate to a multivariate framework. We propose two possible multinormex distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distributi...

Buriticá, Gloria Naveau, Philippe

First, we complement the case study of heavy rainfall in France by implementing Pareto-based methods using declustering techniques. Second, we develop on the asymptotic theory of the stable sums method. To prove Theorem 6.1, we give a more general statement and prove the multivariate central limit theory of regularly varying time series with unit (...

Buriticá, Gloria Naveau, Philippe

Heavy rainfall distributional modeling is essential in any impact studies linked to the water cycle, e.g.\ flood risks. Still, statistical analyses that both take into account the temporal and multivariate nature of extreme rainfall are rare, and often, a complex de-clustering step is needed to make extreme rainfall temporally independent. A natura...