A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space

Ko, Mi-Hwa; Kim, Taesung; Han, Kyung Eun

doi:10.1007/s10959-008-0144-z

Cited by 36 publications

(18 citation statements)

References 9 publications

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“…Ko et al [ 3 ] proved almost sure convergence for H -valued NA random vectors and Thanh [ 6 ] proved almost sure convergence for H -valued NA random vectors and provided extensions of the results in Ko et al [ 3 ]. Miao [ 7 ] showed Hajeck-Renyi inequality for NA random vectors in a Hilbert space.…”

Section: Introductionmentioning

confidence: 98%

“…Ko et al [ 3 ] introduced the concept of negative association (NA) for -valued random vectors. A finite family of -valued random vectors is said to be negatively associated (NA) if for every pair of disjoint nonempty subsets A and B of and any real coordinatewise nondecreasing functions f on , g on , whenever the covariance exists.…”

Section: Introductionmentioning

confidence: 99%

“…Ko et al [ 3 ] extended the concept of negative association in to a Hilbert space as follows. A sequence of H -valued random vectors is said to be NA if for some orthonormal basis of H and for any , the d -dimensional sequence of -valued random vectors is NA.…”

Section: Introductionmentioning

confidence: 99%

“…Huan et al [ 2 ] presented another concept of negative association for H -valued random vectors which is more general than the concept of H -valued NA random vectors introduced by Ko et al [ 3 ] as follows.…”

Section: Introductionmentioning

confidence: 99%

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The complete moment convergence for CNA random vectors in Hilbert spaces

2017

J Inequal Appl

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In this paper we establish the complete moment convergence for sequences of coordinatewise negatively associated random vectors in Hilbert spaces. The result extends the complete moment convergence in (Ko in J. Inequal. Appl. 2016:131, 2016) to Hilbert spaces as well as generalizes the Baum-Katz type theorem in (Huan et al. in Acta Math. Hung. 144(1):132-149, 2014) to the complete moment convergence.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The complete moment convergence for CNA random vectors in Hilbert spaces

2017

J Inequal Appl

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“…Many papers have adopted this tool. We cannot list them all here, but we will just mention a recent paper, by Ko, Kim, and Han [ 16], in which the reader may find further references for the use of positive and negative dependence in obtaining limit theorems.…”

Section: Journal Of Hydrologic Engineeringmentioning

confidence: 99%

The Impact of Lehmann’s Work in Applied Probability

Piegorsch

Shaked

2011

Selected Works of E. L. Lehmann

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Lehmann's works in applied probability crossed a broad spectrum of topics, and many of his papers had substantial impact. We comment on two such examples below. The first [19] provided a valuable beginning for the study and application of notions of positive and negative dependence. The second [20] also touched on issues of probability theory and the nature of random variables-in particular, on the distributional aspects of the reciprocal of a random variable. The contributions each represented are a study in contrasts, however: the former was a substantial work from which many wide-ranging contributions developed, while the second was a shorter, later-appearing piece whose impact(s) are still evolving.

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A new stochastic method based on the Taylor expansion to compute response probability densities of uncertain systems

Navarro‐Quiles

Laudani

Falsone

2022

Numerical Meth Engineering

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In this article, a new stochastic approach is proposed for the analysis of structural systems with uncertainties. This novel strategy method combines the probability transformation method, expressed in terms of characteristic function with a probabilistic version of the Taylor expansion. Some notes about the convergence and the accuracy of the proposed method are reported. The results of these notes and several examples here reported evidence an optimum level of accuracy, coupled with great simplicity of application of this approach, even for relatively high levels of uncertainties. Hence, this method can be considered a valuable tool for the solution of stochastic analyses of engineering systems. Several examples are performed to show the capability of the results established. These applications show how the method is a useful technique for engineering analysis.

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A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space

Cited by 36 publications

References 9 publications

The complete moment convergence for CNA random vectors in Hilbert spaces

The complete moment convergence for CNA random vectors in Hilbert spaces

The Impact of Lehmann’s Work in Applied Probability

A new stochastic method based on the Taylor expansion to compute response probability densities of uncertain systems

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