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Gaussian approximation for functionals of Gibbs particle processes

Daniela Flimmel, Viktor Beneš (2018)

Kybernetika

In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space ℝ d are extended to the space of compact sets on ℝ d equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the...

Gaussian automorphisms whose ergodic self-joinings are Gaussian

Mariusz Lemańczyk, F. Parreau, J. Thouvenot (2000)

Fundamenta Mathematicae

 We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class.  We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors. This...

Gaussian process modeling with inequality constraints

Sébastien Da Veiga, Amandine Marrel (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Gaussian process modeling is one of the most popular approaches for building a metamodel in the case of expensive numerical simulators. Frequently, the code outputs correspond to physical quantities with a behavior which is known a priori: Chemical concentrations lie between 0 and 1, the output is increasing with respect to some parameter, etc. Several approaches have been proposed to deal with such information. In this paper, we introduce a new framework for incorporating constraints in Gaussian...

Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property

Cyril Labbé (2014)

Annales de l'I.H.P. Probabilités et statistiques

We encode the genealogy of a continuous-state branching process associated with a branching mechanism 𝛹 – or 𝛹 -CSBP in short – using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property – the existence of an ancestor from which the entire population descends asymptotically – and give a necessary and sufficient condition on the 𝛹 -CSBP for...

Generalised regular variation of arbitrary order

Edward Omey, Johan Segers (2010)

Banach Center Publications

Let f be a measurable, real function defined in a neighbourhood of infinity. The function f is said to be of generalised regular variation if there exist functions h ≢ 0 and g > 0 such that f(xt) - f(t) = h(x)g(t) + o(g(t)) as t → ∞ for all x ∈ (0,∞). Zooming in on the remainder term o(g(t)) eventually leads to the relation f(xt) - f(t) = h₁(x)g₁(t) + ⋯ + hₙ(x)gₙ(t) + o(gₙ(t)), each g i being of smaller order than its predecessor g i - 1 . The function f is said to be generalised regularly varying of...

Generalized logistic model and its orthant tail dependence

Helena Ferreira, Luisa Pereira (2011)

Kybernetika

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn [14], Joe and Hu [6] and Fougères et al. [3]. The...

Generalized madogram and pairwise dependence of maxima over two regions of a random field

Cecília Fonseca, Luísa Pereira, Helena Ferreira, Ana Paula Martins (2015)

Kybernetika

Spatial environmental processes often exhibit dependence in their large values. In order to model such processes their dependence properties must be characterized and quantified. In this paper we introduce a measure that evaluates the dependence among extreme observations located in two disjoint sets of locations of ℝ 2 . We compute the range of this new dependence measure, which extends the existing λ -madogram concept, and compare it with extremal coefficients, finding generalizations of the known...

Generalized tempered stable processes

Jan Rosiński, Jennifer L. Sinclair (2010)

Banach Center Publications

This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy processes are...

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