Question

Does Uniform Integrability of a product martingale $M$ imply integrability of $\sup|M_n|$?

score 141 · Answer 1 · 2020-08-24 19:15:23

141

Views

Does Uniform Integrability of a product martingale $M$ imply integrability of $\sup|M_n|$?

Published on 24 Aug 2020 - 19:15

score 187 · Answer 2 · 2020-09-01 15:26:40

187

Views

Showing $\{X_n\}$ is uniformly integrable

Published on 01 Sep 2020 - 15:26

score 355 · Answer 3 · 2020-09-02 21:01:52

355

Views

Example of a sequence that is not uniformly integrable.

Published on 02 Sep 2020 - 21:01

score 185 · Answer 4 · 2020-10-04 22:39:20

185

Views

If $\sup_n$ $E|X_n|^{1+\sigma} \lt \infty$ for $\sigma \gt $0, then $\{|X_n|\}$ is uniformly integrable

Published on 04 Oct 2020 - 22:39

score 840 · Answer 5 · 2026-02-23 17:00:09

840

Views

Is the exponential martingale of Brownian motion uniformly absolutely continuous?

Published on 23 Feb 2026 - 17:00

score 134 · Answer 6 · 2020-10-25 18:17:57

134

Views

If $f_n$ is uniformly integrable, then $\lim_{t\to\infty}\int|f_n|I_{|f_n|>t} = 0$ for all $n$

Published on 25 Oct 2020 - 18:17

score 119 · Answer 7 · 2020-10-30 15:03:31

119

Views

If $(X_k)_{k\in\mathbb N}$, show that $\sum_{k=1}^n(X_k-\text E[X_k])$ converges almost surely as $n\to\infty$

Published on 30 Oct 2020 - 15:03

score 104 · Answer 8 · 2020-12-02 02:21:14

104

Views

’s are uniformly integrable if ||^ < ∞

Published on 02 Dec 2020 - 2:21

score 189 · Answer 9 · 2020-12-10 10:53:50

189

Views

stopped UI discrete time martingale is UI

Published on 10 Dec 2020 - 10:53

score 219 · Answer 10 · 2020-12-12 17:05:16

219

Views

Integrable submartingale

Published on 12 Dec 2020 - 17:05

score 105 · Answer 11 · 2020-12-14 12:33:16

105

Views

Confusion on Uniform Integrability of Random Variables

Published on 14 Dec 2020 - 12:33

score 49 · Answer 12 · 2021-01-23 23:36:37

49

Views

Uniform integrability and converging process

Published on 23 Jan 2021 - 23:36

score 204 · Answer 13 · 2021-02-11 18:45:42

204

Views

Family of RV is uniformly integrable iff there is $\phi$ with $\frac{\phi(x)}{x}\rightarrow\infty$ and $\sup_n E(\phi(\vert X_n\vert))<\infty$

Published on 11 Feb 2021 - 18:45

score 65 · Answer 14 · 2021-02-27 14:52:15

65

Views

Limits of an Integral: $\lim_{n\to \infty} \int x^2 \sin\left(f_n(x)\right)\mathrm{d}x=0$

Published on 27 Feb 2021 - 14:52

score 332 · Answer 15 · 2021-02-28 02:14:05

332

Views

Different definition of uniform integrability

Published on 28 Feb 2021 - 2:14

List Question

Does Uniform Integrability of a product martingale $M$ imply integrability of $\sup|M_n|$?

Showing $\{X_n\}$ is uniformly integrable

Example of a sequence that is not uniformly integrable.

If $\sup_n$ $E|X_n|^{1+\sigma} \lt \infty$ for $\sigma \gt $0, then $\{|X_n|\}$ is uniformly integrable

Is the exponential martingale of Brownian motion uniformly absolutely continuous?

If $f_n$ is uniformly integrable, then $\lim_{t\to\infty}\int|f_n|I_{|f_n|>t} = 0$ for all $n$

If $(X_k)_{k\in\mathbb N}$, show that $\sum_{k=1}^n(X_k-\text E[X_k])$ converges almost surely as $n\to\infty$

’s are uniformly integrable if ||^ < ∞

stopped UI discrete time martingale is UI

Integrable submartingale

Confusion on Uniform Integrability of Random Variables

Uniform integrability and converging process

Family of RV is uniformly integrable iff there is $\phi$ with $\frac{\phi(x)}{x}\rightarrow\infty$ and $\sup_n E(\phi(\vert X_n\vert))<\infty$

Limits of an Integral: $\lim_{n\to \infty} \int x^2 \sin\left(f_n(x)\right)\mathrm{d}x=0$

Different definition of uniform integrability

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