Question

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

score 196 · Answer 1 · 2020-02-10 18:21:39

196

Views

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

Published on 10 Feb 2020 - 18:21

score 257 · Answer 2 · 2020-02-18 04:32:15

257

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 18 Feb 2020 - 4:32

score 238 · Answer 3 · 2020-03-02 14:28:28

238

Views

Uniform integrability of product of random variables

Published on 02 Mar 2020 - 14:28

score 55 · Answer 4 · 2020-03-11 12:03:37

55

Views

$\sup L^1$ space with uniform integrability

Published on 11 Mar 2020 - 12:03

score 26 · Answer 5 · 2020-03-25 14:48:47

26

Views

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

Published on 25 Mar 2020 - 14:48

score 78 · Answer 6 · 2020-03-27 17:36:27

78

Views

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

Published on 27 Mar 2020 - 17:36

score 249 · Answer 7 · 2020-03-29 16:38:52

249

Views

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

Published on 29 Mar 2020 - 16:38

score 506 · Answer 8 · 2020-04-20 01:58:05

506

Views

Almost sure convergence implies uniform integrability (Submartingales)

Published on 20 Apr 2020 - 1:58

score 115 · Answer 9 · 2020-04-23 15:01:15

115

Views

using DCT to prove Uniform Integrable

Published on 23 Apr 2020 - 15:01

score 147 · Answer 10 · 2020-05-11 18:42:22

147

Views

Uniform integrability: other definition

Published on 11 May 2020 - 18:42

score 848 · Answer 11 · 2020-05-15 03:26:25

848

Views

Optional Stopping Theorem and Uniform Integrability

Published on 15 May 2020 - 3:26

score 189 · Answer 12 · 2020-05-23 10:50:00

189

Views

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

Published on 23 May 2020 - 10:50

score 73 · Answer 13 · 2020-05-24 22:46:04

73

Views

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

Published on 24 May 2020 - 22:46

score 225 · Answer 14 · 2020-05-28 01:08:23

225

Views

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

Published on 28 May 2020 - 1:08

score 28 · Answer 15 · 2020-05-31 00:19:20

28

Views

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

Published on 31 May 2020 - 0:19

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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