List questions from uniform-integrability

Published on 16 Jul 2018 - 17:22

329

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Optimal Stopping Theorem for UI Martingales

Published on 19 Jul 2018 - 23:22

2.1k

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Uniformly integrable local martingale

Published on 22 Mar 2026 - 9:28

201

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Non-negative uniformly integrable local martingale

Published on 23 Feb 2026 - 2:51

145

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Show that $\text{ sup}_n \int{|f_n|^pdm<C}$ implies $\int_{E}{|f_n|dm}<\epsilon \text{ for large enough } n$.

Published on 11 Aug 2018 - 10:32

1k

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Is a uniformly integrable martingale stopped at every stopping time also uniformly integrable?

Published on 25 Mar 2026 - 8:09

509

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Necessity of uniform integrability in martingale convergence theorem

Published on 14 Sep 2018 - 19:26

162

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Characterization of Martingale and Definition of Uniform Integrability

Published on 25 Mar 2026 - 8:09

457

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Can we interchange integral and limit if the sequence of function is uniformly integrable?

Published on 23 Mar 2026 - 18:46

357

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Proving uniform integrability

Published on 22 Mar 2026 - 0:04

249

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Supremem of Uniformly Integrable Sequences

Published on 22 Mar 2026 - 12:49

78

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Extension of result to stopping times

Published on 22 Mar 2026 - 3:17

721

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A martingale that does not converge in $L^1$

Published on 22 Mar 2026 - 17:59

205

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Show that if $p > 1$ and $\sup_{n \geq 1} |X_n| \in L^p$ then $\{X_n, n \geq 1\}$ is uniformly integrable.

Published on 18 Jan 2019 - 17:23

212

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Is a continuous function of (integrable) Brownian motion always integrable?

Published on 22 Jan 2019 - 9:25

List Question

Example: $\{X_n \}$ is uniformly integrable but $E[ f(X_n) ]=\infty$ with $f(x)=\omega(x)$

Optimal Stopping Theorem for UI Martingales

Uniformly integrable local martingale

Non-negative uniformly integrable local martingale

Show that $\text{ sup}_n \int{|f_n|^pdm<C}$ implies $\int_{E}{|f_n|dm}<\epsilon \text{ for large enough } n$.

Is a uniformly integrable martingale stopped at every stopping time also uniformly integrable?

Necessity of uniform integrability in martingale convergence theorem

Characterization of Martingale and Definition of Uniform Integrability

Can we interchange integral and limit if the sequence of function is uniformly integrable?

Proving uniform integrability

Supremem of Uniformly Integrable Sequences

Extension of result to stopping times

A martingale that does not converge in $L^1$

Show that if $p > 1$ and $\sup_{n \geq 1} |X_n| \in L^p$ then $\{X_n, n \geq 1\}$ is uniformly integrable.

Is a continuous function of (integrable) Brownian motion always integrable?

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