Question

Prove Uniform integrability of $ \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx $

score 87 · Answer 1 · 2026-02-23 03:47:58

87

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Prove Uniform integrability of $ \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx $

Published on 23 Feb 2026 - 3:47

score 1.4k · Answer 2 · 2026-02-23 16:59:42

1.4k

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If $M$ is an $L^2$-bounded continuous local martingale, then $M^2-[M]$ is uniformly integrable

Published on 23 Feb 2026 - 16:59

score 180 · Answer 3 · 2017-06-13 18:03:21

180

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For right continuous martingales and a collection of stopping times, for each $T>0$, $\{X(T\wedge \tau):\tau \in S\}$ is uniformly integrable

Published on 13 Jun 2017 - 18:03

score 117 · Answer 4 · 2017-06-27 02:05:58

117

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Why is this weaker then Uniform Integrability?

Published on 27 Jun 2017 - 2:05

score 809 · Answer 5 · 2017-07-01 08:17:12

809

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Is a sequence of identical distributed integrable random variables even uniformly integrable?

Published on 01 Jul 2017 - 8:17

score 619 · Answer 6 · 2017-08-18 02:40:41

619

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Uniform Integrability of $M^2$ if $M$ is a martingale.

Published on 18 Aug 2017 - 2:40

score 486 · Answer 7 · 2017-08-20 22:48:34

486

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Sufficient Condition for Uniform Integrability $\mathcal{L}^1$-boundedness

Published on 20 Aug 2017 - 22:48

score 99 · Answer 8 · 2017-08-21 22:44:57

99

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"A Master Dominated Convergence Theorem" From Gordan Žitkovic's Probability Theory notes

Published on 21 Aug 2017 - 22:44

score 1k · Answer 9 · 2017-10-11 21:52:03

1k

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$f_n$ uniformly absolutely continuous implies $f_n^+$ uniformly absolutely continuous?

Published on 11 Oct 2017 - 21:52

score 117 · Answer 10 · 2017-11-18 21:27:41

117

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Showing $(X-X_n)^+$ being uniformly integrable and $X_n\rightarrow X$ in $L^1$

Published on 18 Nov 2017 - 21:27

score 56 · Answer 11 · 2017-11-20 07:23:50

56

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Uniform integrability when $\forall g \in \mathcal{L}^1$ there is always an $|f_n|>|g|$

Published on 20 Nov 2017 - 7:23

score 522 · Answer 12 · 2017-11-20 16:50:56

522

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$X_k$ uniformly integrable iff $\lim_{n \to \infty}\limsup_{k\to\infty}\mathbb E(\vert X_k \vert \mathbb 1_{\vert X_k \vert \ge n})=0$

Published on 20 Nov 2017 - 16:50

score 163 · Answer 13 · 2017-11-24 20:25:21

163

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The limit of a quotient of integral moments

Published on 24 Nov 2017 - 20:25

score 219 · Answer 14 · 2017-11-25 02:16:51

219

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If $\{X_n\}_{n\in\mathbb{N}}$ uniformly integrable, is $\{X_n(w)\}_{n\in\mathbb{N}}$ a bounded set for sample path $w$?

Published on 25 Nov 2017 - 2:16

score 1k · Answer 15 · 2017-11-26 19:47:06

1k

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Submartingale inequality

Published on 26 Nov 2017 - 19:47

List Question

Prove Uniform integrability of $ \int_{0}^{\infty} e^{-e^{is}\cdot x^2} dx $

If $M$ is an $L^2$-bounded continuous local martingale, then $M^2-[M]$ is uniformly integrable

For right continuous martingales and a collection of stopping times, for each $T>0$, $\{X(T\wedge \tau):\tau \in S\}$ is uniformly integrable

Why is this weaker then Uniform Integrability?

Is a sequence of identical distributed integrable random variables even uniformly integrable?

Uniform Integrability of $M^2$ if $M$ is a martingale.

Sufficient Condition for Uniform Integrability $\mathcal{L}^1$-boundedness

"A Master Dominated Convergence Theorem" From Gordan Žitkovic's Probability Theory notes

$f_n$ uniformly absolutely continuous implies $f_n^+$ uniformly absolutely continuous?

Showing $(X-X_n)^+$ being uniformly integrable and $X_n\rightarrow X$ in $L^1$

Uniform integrability when $\forall g \in \mathcal{L}^1$ there is always an $|f_n|>|g|$

$X_k$ uniformly integrable iff $\lim_{n \to \infty}\limsup_{k\to\infty}\mathbb E(\vert X_k \vert \mathbb 1_{\vert X_k \vert \ge n})=0$

The limit of a quotient of integral moments

If $\{X_n\}_{n\in\mathbb{N}}$ uniformly integrable, is $\{X_n(w)\}_{n\in\mathbb{N}}$ a bounded set for sample path $w$?

Submartingale inequality

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