Displaying similar documents to “Limiting behavior of the perturbed empirical distribution functions evaluated at U -statistics for strongly mixing sequences of random variables.”

The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in 𝕃 p

Jérôme Dedecker, Florence Merlevède (2007)

ESAIM: Probability and Statistics


Considering the centered empirical distribution function as a variable in 𝕃 p ( μ ) , we derive non asymptotic upper bounds for the deviation of the 𝕃 p ( μ ) -norms of as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

Relativization of some aspects of the theory of functions of bounded variation

Krishna M. Garg


We present here relativized versions of some aspects of the theory of functions of bounded variation, viz. relative to a function of bounded variation, without going into relative bounded variation. A few results have been known in this direction for some time when the functions involved are continuous, but due to the complications that arise when the functions are discontinuous, no systematic attempt seems to have been made in this direction in the past.Let B denote the linear space...

Sojourn times.

Takács, Lajos (1996)

Journal of Applied Mathematics and Stochastic Analysis