On weak dependence conditions: The case of discrete valued processes

2012 ◽  
Vol 82 (11) ◽  
pp. 1941-1948 ◽  
Author(s):  
Paul Doukhan ◽  
Konstantinos Fokianos ◽  
Xiaoyin Li
Keyword(s):  
Weak Dependence ◽  
Dependence Conditions

Rates of convergence in some SLLN under weak dependence conditions

2010 ◽  
Vol 76 (3-4) ◽  
pp. 683-695
Author(s):  
Paul Doukhan ◽  
Oleg Klesov ◽  
Gabriel Lang
Keyword(s):  
Rates Of Convergence ◽  
Weak Dependence ◽  
Dependence Conditions

scholarly journals An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

2017 ◽  
Vol 71 (1) ◽  
pp. 11
Author(s):  
Marcin Dudziński
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Empirical Process ◽  
Weak Dependence ◽  
Dependence Conditions

Let: \(\mathbf{Y=}\left( \mathbf{Y}_{i}\right)\), where \(\mathbf{Y}_{i}=\left( Y_{i,1},...,Y_{i,d}\right)\), \(i=1,2,\dots \), be a \(d\)-dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf \(F\), and \(F_{n}\left( \mathbf{x}\right) :=\frac{1}{n}\sum_{i=1}^{n}\mathbb{I}\left(Y_{i,1}\leq x_{1},\dots ,Y_{i,d}\leq x_{d}\right)\) denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process \(B_{n}=\sqrt{n}\left( F_{n}-F\right)\) under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.

On weak dependence conditions for Poisson autoregressions

2012 ◽  
Vol 82 (5) ◽  
pp. 942-948 ◽  
Author(s):  
Paul Doukhan ◽  
Konstantinos Fokianos ◽  
Dag Tjøstheim
Keyword(s):  
Weak Dependence ◽  
Dependence Conditions

Phase Inversion in Two-Phase Liquid Systems

1992 ◽  
Vol 57 (7) ◽  
pp. 1419-1423
Author(s):  
Jindřich Weiss
Keyword(s):  
Interfacial Tension ◽  
Phase Inversion ◽  
Continuous Phase ◽  
Considerable Effect ◽  
Weak Dependence ◽  
Dispersed Phase ◽  
Two Phase ◽  
Liquid Systems ◽  
Phase Liquid

New data on critical holdups of dispersed phase were measured at which the phase inversion took place. The systems studied differed in the ratio of phase viscosities and interfacial tension. A weak dependence was found of critical holdups on the impeller revolutions and on the material contactor; on the contrary, a considerable effect of viscosity was found out as far as the viscosity of continuous phase exceeded that of dispersed phase.

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