Displaying similar documents to “The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in 𝕃 p ”

Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences

Jérôme Dedecker, Sana Louhichi (2005)

ESAIM: Probability and Statistics

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We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit....

Generalized covariance inequalities

Przemysław Matuła, Maciej Ziemba (2011)

Open Mathematics

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We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2001)

ESAIM: Probability and Statistics

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We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform φ -mixing random fields, we require both finite fourth moments and an algebraic decay of the...