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Defects and transformations of quasi-copulas

Michal Dibala, Susanne Saminger-Platz, Radko Mesiar, Erich Peter Klement (2016)

Kybernetika

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being...

Density in small time for Lévy processes

Jean Picard (2010)

ESAIM: Probability and Statistics

The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process cannot...

Detecting abrupt changes in random fields

Antoine Chambaz (2002)

ESAIM: Probability and Statistics

This paper is devoted to the study of some asymptotic properties of a M -estimator in a framework of detection of abrupt changes in random field’s distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M -estimation method, concentration inequalities, maximal inequalities for dependent random variables and φ -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild,...

Detecting abrupt changes in random fields

Antoine Chambaz (2010)

ESAIM: Probability and Statistics

This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under...

Determinantal probability measures

Russell Lyons (2003)

Publications Mathématiques de l'IHÉS

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation,...

Dispersive functions and stochastic orders

Jarosław Bartoszewicz (1997)

Applicationes Mathematicae

Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented

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