Results 41 to 50 of about 1,210 (131)
Open Mathematics, 2017 Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’
Dudziński Marcin, Furmańczyk Konrad
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A class of small deviation theorems for the random fields on an m rooted Cayley tree
, 2012 In this paper, we are to establish a class of strong deviation theorems for the random fields relative to m th-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree.
Zhiyan Shi +3 more
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International Journal of Stochastic Analysis, Volume 13, Issue 3, Page 261-267, 2000., 2000 Let X1, …, Xn be negatively dependent uniformly bounded random variables with d.f. F(x). In this paper we obtain bounds for the probabilities P(|∑i=1nXi|≥nt) and P(|ξˆpn−ξp|>ϵ) where ξˆpn is the sample pth quantile and ξp is the pth quantile of F(x). Moreover, we show that ξˆpn is a strongly consistent estimator of ξp under mild restrictions on F(x) in
M. Amini, A. Bozorgnia
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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
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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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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
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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
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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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, 2012 Let X, X1, X2,... be a sequence of independent and identically distributed random variables in the domain of attraction of a normal distribution. A universal result in almost sure limit theorem for the self-normalized partial sums Sn/Vnis established ...
Qunying Wu
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Complete convergence for weighted sums of arrays of rowwise ρ˜-mixing random variables
Journal of Inequalities and Applications, 2013 Let {Xni,i≥1,n≥1} be an array of rowwise ρ˜-mixing random variables. Some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ˜-mixing random variables are presented without assumptions of identical distribution.
A. Shen, R. Wu, Xinghui Wang, Yan Shen
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