Results 31 to 40 of about 1,018 (114)
A strong law of large numbers for capacities
, 2005 We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random ...
Maccheroni, Fabio, Marinacci, Massimo
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A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law [PDF]
, 2013 In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law.
Giuliano, Rita, Szewczak, Zbigniew S.
core +2 more sources
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 171-177, 1999., 1999 Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn| ≥ t} ≤ P{|X| ≥ t} for all nonnegative real numbers t and , for 1 < p < 2, then we prove that Under the weak condition of E|X|plog+|X| < ∞, it converges to 0 in L1. And the results can be generalized to an r‐dimensional array of random variables under the conditions ...
Dug Hun Hong, Seok Yoon Hwang
wiley +1 more source
On complete convergence for randomly indexed sums for a case without identical distributions
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 773-782, 1997., 1996 In this note we extend the complete convergence for randomly indexed sums given by Klesov (1989) to nonidentical distributed random variables.
Anna Kuczmaszewska, Dominik Szynal
wiley +1 more source
Higher-order expansions of powered extremes of normal samples
, 2016 In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants.
Ling, Chengxiu, Zhou, Wei
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International Journal of Stochastic Analysis, Volume 10, Issue 1, Page 3-20, 1997., 1996 We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic for a class of strongly mixing sequences of random variables {Xi, i ≥ 1}. Stationarity is not assumed. Here is the perturbed empirical distribution function and Un is a U‐statistic based on X1, …, Xn.
Shan Sun, Ching-Yuan Chiang
wiley +1 more source
Successive normalization of rectangular arrays
, 2013 Standard statistical techniques often require transforming data to have mean $0$ and standard deviation $1$. Typically, this process of "standardization" or "normalization" is applied across subjects when each subject produces a single number.
Olshen, Richard A., Rajaratnam, Bala
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On complete convergence of the sum of a random number of a stable type P random elements
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 33-36, 1995., 1993 Complete convergence for randomly indexed normalized sums of random elements of the form is established. The random elements {Xn} belong to a type p stable space and are assumed to be independent, but not necessarily identically distributed. No assumptions are placed on the joint distributions of the stopping times {Tn}.
André Adler, Andrey Volodin
wiley +1 more source
A strong law of large numbers for independent compactly uniformly integrable random sets [PDF]
Arab Journal of Mathematical SciencesPurposeThe aim of this work is to prove a strong law of large numbers for a sequence of independent compactly uniformly integrable random sets with values in the family of convex closed subsets of a separable Banach space E, again without requiring any ...
Mohammed El Allali +2 more
doaj +1 more source
Kolmogorov's law of the iterated logarithm for noncommutative martingales
, 2014 We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout.
Zeng, Qiang
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