On uniform nonintegrability for a sequence of random variables

Chandra, Tapas K.; Hu, Tien-Chung; Rosalsky, Andrew

doi:10.1016/j.spl.2016.04.015

Cited by 4 publications

(30 citation statements)

References 7 publications

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“…In this section, we borrow two examples from [2] to illustrate some phenomena. The first example shows that UNI is strictly stronger than W-UNI in general.…”

Section: Two Examplesmentioning

confidence: 99%

“…Next, we give a characterization on W-UNI, which corresponds to [2,Theorem 3.3], and can be regarded as a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. Proof.…”

Section: It Follows Thatmentioning

confidence: 99%

“…In virture of (1.1), the authors of [2] gave the following definition: In virture of (1.3), we give the following definition.…”

Section: Introductionmentioning

confidence: 99%

“…By Definition 1.2, we can easily get that {X n , n ≥ 1} is W-UNI. But [2,Example 4.1] shows that we cann't conclude that {X n , n ≥ 1} is UNI.…”

Section: Introductionmentioning

confidence: 99%

“…In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised in [2].…”

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confidence: 99%

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Uniform nonintegrability of random variables

Xue

2017

Front. Math. China

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In a recent paper [2], Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. In addition, we give some remarks, one of which gives a negative answer to the open problem raised in [2].

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“…In this section, we borrow two examples from [2] to illustrate some phenomena. The first example shows that UNI is strictly stronger than W-UNI in general.…”

Section: Two Examplesmentioning

confidence: 99%

Section: It Follows Thatmentioning

confidence: 99%

“…In virture of (1.1), the authors of [2] gave the following definition: In virture of (1.3), we give the following definition.…”

Section: Introductionmentioning

confidence: 99%

“…By Definition 1.2, we can easily get that {X n , n ≥ 1} is W-UNI. But [2,Example 4.1] shows that we cann't conclude that {X n , n ≥ 1} is UNI.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Uniform nonintegrability of random variables

Xue

2017

Front. Math. China

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On Uniform Nonintegrability and Weak Uniform Nonintegrability of a Sequence of Random Variables with Respect to a Nonnegative Array

Chandra

Rosalsky

2021

Calcutta Statistical Association Bulletin

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Chandra, Hu and Rosalsky [1] introduced the notion of a sequence of random variables being uniformly nonintegrable and they established a de La Vallée Poussin type criterion for this notion. Inspired by the Chandra, Hu and Rosalsky [1] article, Hu and Peng [2] introduced the weaker notion of a sequence of random variables being weakly uniformly nonintegrable and they also established a de La Vallée Poussin type criterion for this notion using a modification of the Chandra, Hu and Rosalsky [1] argument. In this correspondence, we introduce the more general notion of uniform nonintegrability and weak uniform nonintegrability with respect to an array of nonnegative real numbers together with a de La Vallée Poussin type criterion for this notion. This criterion immediately yields as particular cases the criteria of Chandra, Hu and Rosalsky [1] and Hu and Peng [2] , and it has a substantially simpler and more straightforward proof.

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On B-statistical uniform nonintegrability of a sequence of random variables

Chen,

Li,

Wang

et al. 2023

Filomat

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In this paper, we introduce a notion of B-statistical uniform nonintegrability with respect to A (B-UNI(c) w.r.t. A, in short), which is weaker than UNI(c) w.r.t. A (see [3]). We establish the de La Vall?e Poussin criterion for B-UNI(c) w.r.t. A, which extends Theorem 2.1 of Chandra et al. (2021) [3]. Moreover, we also give a necessary condition for the sequence of random variables {Xk, k ? N} to be B-UNI(c) w.r.t. A.

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On uniform nonintegrability for a sequence of random variables

Cited by 4 publications

References 7 publications

Uniform nonintegrability of random variables

Uniform nonintegrability of random variables

On Uniform Nonintegrability and Weak Uniform Nonintegrability of a Sequence of Random Variables with Respect to a Nonnegative Array

On B-statistical uniform nonintegrability of a sequence of random variables

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