Question

Uniformly integrable sequence tending to 0 a.s. but with $\mathbb{E}(\sup_n|X_n|) = \infty$

score 799 · Answer 1 · 2013-12-03 19:49:40

799

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Uniformly integrable sequence tending to 0 a.s. but with $\mathbb{E}(\sup_n|X_n|) = \infty$

Published on 03 Dec 2013 - 19:49

score 77 · Answer 2 · 2013-12-11 01:34:02

77

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Convergence in mean with logarithm

Published on 11 Dec 2013 - 1:34

score 380 · Answer 3 · 2013-12-23 17:01:13

380

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Uniform integrability of a set of measurable functions (show an equivalence)

Published on 23 Dec 2013 - 17:01

score 96 · Answer 4 · 2013-12-23 23:52:01

96

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If $P(X=k)=1/2^k$ for every $k\ge1$ and $h_k(x)$ converges to identity function $h(x)=x$, does $E(X|h_k(X))$ converge almost surely?

Published on 23 Dec 2013 - 23:52

score 686 · Answer 5 · 2013-12-24 11:36:32

686

Views

Uniform integrability (show an equivalence)

Published on 24 Dec 2013 - 11:36

score 2.5k · Answer 6 · 2013-12-26 12:31:38

2.5k

Views

Does uniform integrability plus convergence in measure imply convergence in $L^1$?

Published on 26 Dec 2013 - 12:31

score 2.5k · Answer 7 · 2014-01-12 20:14:51

2.5k

Views

Local martingale is locally uniformly integrable martingale?

Published on 12 Jan 2014 - 20:14

score 1.3k · Answer 8 · 2014-01-14 19:18:11

1.3k

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Is a compensated Poisson process uniformly integrable

Published on 14 Jan 2014 - 19:18

score 876 · Answer 9 · 2014-02-09 22:24:26

876

Views

Is the product of two independent uniform integrable random variable is uniform integrable?

Published on 09 Feb 2014 - 22:24

score 306 · Answer 10 · 2014-02-11 14:37:34

306

Views

Show the equi-integrability of a finite set of $\mathcal{L}_{\mu}^1$-functions

Published on 11 Feb 2014 - 14:37

score 268 · Answer 11 · 2014-02-14 00:08:50

268

Views

Optional Sampling a.s. finite stopping time

Published on 14 Feb 2014 - 0:08

score 192 · Answer 12 · 2014-02-20 10:32:21

192

Views

Equivalent condition for equi-integrability

Published on 20 Feb 2014 - 10:32

score 1k · Answer 13 · 2014-02-20 16:39:21

1k

Views

Convergence of expectations under almost everywhere convergence and uniform integrability

Published on 20 Feb 2014 - 16:39

score 332 · Answer 14 · 2017-04-25 16:34:21

332

Views

Convergence of $r$th moment implies uniform integrability (Chung Theorem 4.5.4.)

Published on 25 Apr 2017 - 16:34

score 380 · Answer 15 · 2017-05-08 22:23:13

380

Views

Show that $X_t=\exp(B_t - t/2)$ converges to $0$ in probability but not uniformly integrable

Published on 08 May 2017 - 22:23

List Question

Uniformly integrable sequence tending to 0 a.s. but with $\mathbb{E}(\sup_n|X_n|) = \infty$

Convergence in mean with logarithm

Uniform integrability of a set of measurable functions (show an equivalence)

If $P(X=k)=1/2^k$ for every $k\ge1$ and $h_k(x)$ converges to identity function $h(x)=x$, does $E(X|h_k(X))$ converge almost surely?

Uniform integrability (show an equivalence)

Does uniform integrability plus convergence in measure imply convergence in $L^1$?

Local martingale is locally uniformly integrable martingale?

Is a compensated Poisson process uniformly integrable

Is the product of two independent uniform integrable random variable is uniform integrable?

Show the equi-integrability of a finite set of $\mathcal{L}_{\mu}^1$-functions

Optional Sampling a.s. finite stopping time

Equivalent condition for equi-integrability

Convergence of expectations under almost everywhere convergence and uniform integrability

Convergence of $r$th moment implies uniform integrability (Chung Theorem 4.5.4.)

Show that $X_t=\exp(B_t - t/2)$ converges to $0$ in probability but not uniformly integrable

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