Related papers: Master equations for extremal models
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
Extreme weather events have an enormous impact on society and are expected to become more frequent and severe with climate change. In this context, resilience planning becomes crucial for risk mitigation and coping with these extreme…
The behavior of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
The extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances. In the dynamical systems framework, it provides important information about the dynamics of the underlying systems. In…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain…
Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…
By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…
We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…
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…
The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes,…
This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…