Related papers: Maxima of moving maxima of continuous functions

We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal…

This paper provides the basis for new methods of inference for max-stable processes \xi\ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process…

For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay,…

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…

Suppose $(f,\mathcal{X},\nu)$ is a measure preserving dynamical system and $\phi:\mathcal{X}\to\mathbb{R}$ is an observable with some degree of regularity. We investigate the maximum process $M_n:=\max\{X_1,\ldots,X_n\}$, where…

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite…

Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge…

We derive a functional limit theorem for the partial maxima process based on a long memory stationary $\alpha$-stable process. The length of memory in the stable process is parameterized by a certain ergodic-theoretical parameter in an…

In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…

The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan \emph{et al.} allows to also account for asymptotic independence. In this paper we introduce…

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…

For each $n\geq 1$, let $ {X_{in}, \quad i \geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima…

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on $m$-dependent approximation for stationary processes and a moderate deviation result.

Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…

Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…

Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions…

The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number of independent random variables among the collection $\{X_t\}_{t\in A}$. We introduce…

We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…