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On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

German Bernhart, Jan-Frederik Mai, Matthias Scherer (2015)

Dependence Modeling

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper...

On the continuity of invariant statistics

Nguyen Van Ho (1978)

Aplikace matematiky

The aim of this paper is to establish theorems on the absolute continuity of translation as well as scale invariant statistics in general, from which the related results by Hodges-Lehmann and Puri-Sen follow. The continuity relations between the joint cdf of a random vector and its marginal cdf's are also considered.

On the control of the difference between two Brownian motions: a dynamic copula approach

Thomas Deschatre (2016)

Dependence Modeling

We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right...

On the control of the difference between two Brownian motions: an application to energy markets modeling

Thomas Deschatre (2016)

Dependence Modeling

We derive a model based on the structure of dependence between a Brownian motion and its reflection according to a barrier. The structure of dependence presents two states of correlation: one of comonotonicity with a positive correlation and one of countermonotonicity with a negative correlation. This model of dependence between two Brownian motions B1 and B2 allows for the value of [...] to be higher than 1/2 when x is close to 0, which is not the case when the dependence is modeled by a constant...

On the convergence of extreme distributions under power normalization

E. M. Nigm (2008)

Applicationes Mathematicae

This paper deals with the convergence in distribution of the maximum of n independent and identically distributed random variables under power normalization. We measure the difference between the actual and asymptotic distributions in terms of the double-log scale. The error committed when replacing the actual distribution of the maximum under power normalization by its asymptotic distribution is studied, assuming that the cumulative distribution function of the random variables is known. Finally,...

On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

Peggy Cénac (2013)

ESAIM: Probability and Statistics

We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as estimation...

On the convergence of the Bhattacharyya bounds in the multiparametric case

Abdulghani Alharbi (1994)

Applicationes Mathematicae

Shanbhag (1972, 1979) showed that the diagonality of the Bhattacharyya matrix characterizes the set of normal, Poisson, binomial, negative binomial, gamma or Meixner hypergeometric distributions. In this note, using Shanbhag's techniques, we show that if a certain generalized version of the Bhattacharyya matrix is diagonal, then the bivariate distribution is either normal, Poisson, binomial, negative binomial, gamma or Meixner hypergeometric. Bartoszewicz (1980) extended the result of Blight and...

On the convergence of the ensemble Kalman filter

Jan Mandel, Loren Cobb, Jonathan D. Beezley (2011)

Applications of Mathematics

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and L p bounds on the ensemble then give L p convergence.

On the curvature of the space of qubits

Attila Andai (2006)

Banach Center Publications

The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone...

On the density of some Wiener functionals: an application of Malliavin calculus.

Antoni Sintes Blanc (1992)

Publicacions Matemàtiques

Using a representation as an infinite linear combination of chi-square independent random variables, it is shown that some Wiener functionals, appearing in empirical characteristic process asymptotic theory, have densities which are tempered in the properly infinite case and exponentially decaying in the finite case.

Currently displaying 361 – 380 of 654