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Bivariate copulas, norms and non-exchangeability

Pier Luigi Papini (2015)

Dependence Modeling

The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.

Bivariate copulas: Transformations, asymmetry and measures of concordance

Sebastian Fuchs, Klaus D. Schmidt (2014)

Kybernetika

The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the...

Block distribution in random strings

Peter J. Grabner (1993)

Annales de l'institut Fourier

For almost all infinite binary sequences of Bernoulli trials ( p , q ) the frequency of blocks of length k ( N ) in the first N terms tends asymptotically to the probability of the blocks, if k ( N ) increases like log 1 p N - log 1 p N - ψ ( N ) (for p q ) where ψ ( N ) tends to + . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case p = q = 1 2 .

BMO and commutators of martingale transforms

Svante Janson (1981)

Annales de l'institut Fourier

The commutator of multiplication by a function and a martingale transform of a certain type is a bounded operator on L p , 1 < p < , if and only if the function belongs to BMO. This is a martingale version of a result by Coifman, Rochberg and Weiss.

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