stochastic compactness
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1995 ◽  
Vol 45 (1-2) ◽  
pp. 81-90 ◽  
Author(s):  
Sándor Csörgö ◽  
David M. Mason

Author(s):  
L. de Hann ◽  
S. I. Resnick

AbstractWe show that stochastic compactness of partial sums with no normal limit distribution corresponds to stochastic compactness of the point processes generated by the observations so that there exist joint limit distributions for the sample sums and the sample maxima.


Author(s):  
R. A. Maller

AbstractThe aim of this paper is to show that some of the known properties of distributions in the domain of attraction of a stable law have counterparts for distributions which are stochastically compact in the sense of Feller. This enables us to unify the ideas of Feller and Doeblin, who first studied the concept of stochastic compactness, and give new characterizations of stochastic compactness and the domain of attraction of the normal distribution.


1979 ◽  
Vol 28 (4) ◽  
pp. 499-509 ◽  
Author(s):  
R. A. Maller

AbstractA recent result of Rogozin on the relative stability of a distribution function is extended, by giving equivalences for relative stability in terms of truncated moments of the distribution and in terms of the real and imaginary parts of the characteristic function. As an application, the known results on centering distributions in the domain of attraction of a stable law are extended to the case of stochastically compact distributions.


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