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One sided strong laws for random variables with infinite mean

100%
Adler A.
Open Mathematics
|
2017
|
tom 15
|
nr 1
828-832
EN
This paper establishes conditions that secure the almost sure upper and lower bounds for a particular normalized weighted sum of independent nonnegative random variables. These random variables do not possess a finite first moment so these results are not typical. These mild conditions allow us to show that the almost sure upper limit is infinity while the almost sure lower bound is one.
2
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Complete convergence for weighted sums of pairwise independent random variables

100%
Ge L., Liu S., Miao Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
467-476
EN
In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.
3
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Various limit theorems for ratios from the uniform distribution

81%
Miao Y., Sun Y., Wang R., Dong M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
393-403
EN
In this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.
4
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Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima

61%
Dudziński M., Furmańczyk K.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1024-1034
EN
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.’s (X1, ...,Xn) has the Archimedean copula CΨ.
5
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On the asymptotic form of convex hulls of Gaussian random fields

61%
Davydov Y., Paulauskas V.
Open Mathematics
|
2014
|
tom 12
|
nr 5
711-720
EN
We consider a centered Gaussian random field X = {X t : t ∈ T} with values in a Banach space $$\mathbb{B}$$ defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = conv{X t : t ∈ T n}, where (T n) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b n)n≥1 with probability 1, (in the sense of Hausdorff distance), where the limit set is the concentration ellipsoid of . The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.
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