Related papers: Representations of max-stable processes based on s…
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…
In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in $C\left([0,1]^k\right)$ by interpolating its realizations at finitely many points is proposed. The…
For the moving average process $X_n=\rho \xi_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\ge -1}$ is an i.i.d. sequence of normally distributed random variables, we study the persistence probabilities…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
This article summarizes the contribution of team genEVA to the EVA (2023) Conference Data Challenge. The challenge comprises four individual tasks, with two focused on univariate extremes and two related to multivariate extremes. In the…
The upcrossings index $0\leq \eta\leq 1,$ a measure of the degree of local dependence in the upcrossings of a high level by a stationary process, plays, together with the extremal index $\theta,$ an important role in extreme events…
The Brown-Resnick max-stable process has proven to be well-suited for modeling extremes of complex environmental processes, but in many applications its likelihood function is intractable and inference must be based on a composite…
We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we…
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…
This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
Machine learning models play a vital role in the prediction task in several fields of study. In this work, we utilize the ability of machine learning algorithms to predict the occurrence of extreme events in a nonlinear mechanical system.…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…
The maxima and the minima of a randomly stopped sample of a random variable, $X$, together with two newly defined random variables that make $X$ into the maxima or minima of a randomly stopped sample of them, can be used to define…
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…