Related papers: A comparative tour through the simulation algorith…
The statistical modelling of spatial extremes has recently made major advances. Much of its focus so far has been on the modelling of the magnitudes of extreme events but little attention has been paid on the timing of extremes. To address…
Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory. Statistical inference for such models is complicated by the…
The structure of stationary first order max-autoregressive schemes with max-semi-stable marginals is studied. A connection between semi-selfsimilar extremal processes and this max-autoregressive scheme is discussed resulting in their…
In risk management it is desirable to grasp the essential statistical features of a time series representing a risk factor. This tutorial aims to introduce a number of different stochastic processes that can help in grasping the essential…
Several application domains require formal but flexible approaches to the comparison problem. Different process models that cannot be related by behavioral equivalences should be compared via a quantitative notion of similarity, which is…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
We prove that the class of discrete time stationary max-stable process satisfying the Markov property is equal, up to time reversal, to the class of stationary max-autoregressive processes of order $1$. A similar statement is also proved…
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…
Recently the regular conditional distributions of max-infinitely divisible processes were derived by \citet{Dombry2011} and although these conditional distributions have complicated closed forms, \citet{Dombry2011b} introduce an algorithm…
Simulators are a critical component of modern robotics research. Strategies for both perception and decision making can be studied in simulation first before deployed to real world systems, saving on time and costs. Despite significant…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent…
We propose a way how to generate a max-stable process in $C[0,1]$ from a max-stable random vector in $\mathbb R^d$ by generalizing the \emph{max-linear model} established by \citet{wansto11}. It turns out that if the random vector follows…
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…
In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by $\alpha$-stable processes, which are used to estimate the effect that the fast…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
This paper contributes to the solution of the problem of transforming a process model with an arbitrary topology into an equivalent structured process model. In particular, this paper addresses the subclass of process models that have no…
Co-simulation is a promising approach for the modelling and simulation of complex systems, that makes use of mature simulation tools in the respective domains. It has been applied in wildly different domains, oftentimes without a…