Related papers: Complete convergence and records for dynamically g…
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…
The Extremal Index is a parameter that measures the intensity of clustering of rare events and is usually equal to the reciprocal of the mean of the limiting cluster size distribution. We show how to build dynamically generated stochastic…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal observations of such time series…
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…
We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…
The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
Motivated by examples from extreme value theory we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
The impact of an extreme climate event depends strongly on its geographical scale. Max-stable processes can be used for the statistical investigation of climate extremes and their spatial dependencies on a continuous area. Most existing…
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its…
To account for volatile renewable energy supply, energy systems optimization problems require high temporal resolution. Many models use time-series clustering to find representative periods to reduce the amount of time-series input data and…
We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…
We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…