Question

If $\mathbb E[\sup_{t\in [0,T]}|X_t|]<\infty$, is $(X_t)_{t\in [0,T]}$ uniformly integrable?

score 198 · Answer 1 · 2026-04-15 12:09:47

198

Views

If $\mathbb E[\sup_{t\in [0,T]}|X_t|]<\infty$, is $(X_t)_{t\in [0,T]}$ uniformly integrable?

Published on 15 Apr 2026 - 12:09

score 260 · Answer 2 · 2026-04-14 04:03:56

260

Views

Is $Y_n := \prod_1^n \xi_i$ for $\xi_i$ i.i.d. $\text{Unif}(0,2)$ a sequence of uniformly integrable random variables?

Published on 14 Apr 2026 - 4:03

score 241 · Answer 3 · 2026-04-15 08:51:24

241

Views

Uniform integrability of product of random variables

Published on 15 Apr 2026 - 8:51

score 58 · Answer 4 · 2026-04-16 23:01:40

58

Views

$\sup L^1$ space with uniform integrability

Published on 16 Apr 2026 - 23:01

score 29 · Answer 5 · 2026-04-12 13:47:12

29

Views

How are these conditions in the definition of uniform integrability different from eachother

Published on 12 Apr 2026 - 13:47

score 81 · Answer 6 · 2026-04-16 04:30:06

81

Views

Appling a density function to a sequence of a.s. converging UI random variables

Published on 16 Apr 2026 - 4:30

score 252 · Answer 7 · 2026-04-15 16:29:05

252

Views

Prove that each sequence of a r.v. is uniformly integrable if $\sup\{ \mathbb{E}(|X_n|^{1+\delta})\}$ is finite

Published on 15 Apr 2026 - 16:29

score 509 · Answer 8 · 2026-04-16 07:00:56

509

Views

Almost sure convergence implies uniform integrability (Submartingales)

Published on 16 Apr 2026 - 7:00

score 118 · Answer 9 · 2026-04-15 09:47:43

118

Views

using DCT to prove Uniform Integrable

Published on 15 Apr 2026 - 9:47

score 150 · Answer 10 · 2026-04-11 08:05:18

150

Views

Uniform integrability: other definition

Published on 11 Apr 2026 - 8:05

score 851 · Answer 11 · 2026-04-16 07:16:35

851

Views

Optional Stopping Theorem and Uniform Integrability

Published on 16 Apr 2026 - 7:16

score 192 · Answer 12 · 2026-04-14 09:24:14

192

Views

A question about proof of Martingale Convergence Theorem. Why does the Uniform integrability imply the following fact?

Published on 14 Apr 2026 - 9:24

score 76 · Answer 13 · 2026-04-16 07:49:46

76

Views

From $(1)$ and $(2)$, t $\{f_n\}$ has a subsequence equivalent to a uniformly integrable sequence.

Published on 16 Apr 2026 - 7:49

score 228 · Answer 14 · 2026-04-15 22:49:46

228

Views

Proving uniformly integrablility of $\{X_n\}$, if $\sup_{n\geq 1} E[f(|X_n|)]<\infty.$

Published on 15 Apr 2026 - 22:49

score 31 · Answer 15 · 2026-04-14 15:54:12

31

Views

Why without loss of generality $\{f_n\}$ et $\{g_n\}$ are uniformly integrable over $A$?

Published on 14 Apr 2026 - 15:54

List Question

If $\mathbb E[\sup_{t\in [0,T]}|X_t|]<\infty$, is $(X_t)_{t\in [0,T]}$ uniformly integrable?

Is $Y_n := \prod_1^n \xi_i$ for $\xi_i$ i.i.d. $\text{Unif}(0,2)$ a sequence of uniformly integrable random variables?

Uniform integrability of product of random variables

$\sup L^1$ space with uniform integrability

How are these conditions in the definition of uniform integrability different from eachother

Appling a density function to a sequence of a.s. converging UI random variables

Prove that each sequence of a r.v. is uniformly integrable if $\sup\{ \mathbb{E}(|X_n|^{1+\delta})\}$ is finite

Almost sure convergence implies uniform integrability (Submartingales)

using DCT to prove Uniform Integrable

Uniform integrability: other definition

Optional Stopping Theorem and Uniform Integrability

A question about proof of Martingale Convergence Theorem. Why does the Uniform integrability imply the following fact?

From $(1)$ and $(2)$, t $\{f_n\}$ has a subsequence equivalent to a uniformly integrable sequence.

Proving uniformly integrablility of $\{X_n\}$, if $\sup_{n\geq 1} E[f(|X_n|)]<\infty.$

Why without loss of generality $\{f_n\}$ et $\{g_n\}$ are uniformly integrable over $A$?

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