Related papers: Master equations for extremal models
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
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 article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…
We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model…
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…
In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…
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…
A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…
Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
Master equations describe the quantum dynamics of open systems interacting with an environment. They play an increasingly important role in understanding the emergence of semiclassical behavior and the generation of entropy, both being…
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 occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
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…
Considered here is one quite general problem about description of extremal configurations maximizing the product of inner radii non-overlapping domains.
Extreme weather is one of the main mechanisms through which climate change will directly impact human society. Coping with such change as a global community requires markedly improved understanding of how global warming drives extreme…
The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…