List questions from martingales

Published on 31 Mar 2026 - 12:16

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For a martingale $X$ does uniform integrability imply integrability of $\sup |X_{n}|$?

Published on 06 Mar 2026 - 3:17

268

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Can I swap conditional expectation and limit

Published on 03 Apr 2026 - 2:10

108

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Martingale (stochastic analysis)

Published on 02 Apr 2026 - 12:55

213

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What is the Benefit If a Stochastic Process is a Submartingale?

Published on 30 Nov 2015 - 6:45

394

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Is this $X_T$ if the stopping time is $T \le \infty$?

Published on 30 Mar 2026 - 0:00

421

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Almost sure convergence of a martingale

Published on 03 Apr 2026 - 10:11

152

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Show that $\sup_n \mathbb{E}(|S_n|)<\infty$ implies $\mathbb{E} \left( \sup_n |S_n| \right)<\infty$ for $S_n=\sum_{k=1}^n X_k$ with $X_k$ iid

Published on 03 Dec 2015 - 2:01

744

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$\max (X_t, a)$ is not a martingale, counterexample

Published on 03 Dec 2015 - 18:16

271

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Show that $E[X_T | T < \infty] \le E[X_0]$ and $cP(\sup X_n \ge c) \le E[X_0]$

Published on 29 Mar 2026 - 23:59

237

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Symmetric Random Walk / Prove $S = \inf\{n : X_n = 7\}$ and $T = 10^{12} \wedge S$ are $\{\mathscr F_n^Y\}$-stopping times.

Published on 30 Mar 2026 - 0:04

321

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Symmetric Random Walk / Find $E[X_S]$ and $E[X_T]$

Published on 30 Mar 2026 - 0:04

345

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Asymmetric Random Walk / Prove $E[X_{T \wedge n}] = (p-q)E[T \wedge n]$

Published on 29 Mar 2026 - 23:59

87

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Convergence result of a UI martingale

Published on 05 Dec 2015 - 10:17

1.4k

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Asymmetric Random Walk / Prove $E[T] = \frac{b}{p-q}$ / How do I use hint?

Published on 30 Mar 2026 - 0:00

List Question

Show that a martingale is not $L^1$ convergent

For a martingale $X$ does uniform integrability imply integrability of $\sup |X_{n}|$?

Can I swap conditional expectation and limit

Martingale (stochastic analysis)

What is the Benefit If a Stochastic Process is a Submartingale?

Is this $X_T$ if the stopping time is $T \le \infty$?

Almost sure convergence of a martingale

Show that $\sup_n \mathbb{E}(|S_n|)<\infty$ implies $\mathbb{E} \left( \sup_n |S_n| \right)<\infty$ for $S_n=\sum_{k=1}^n X_k$ with $X_k$ iid

$\max (X_t, a)$ is not a martingale, counterexample

Show that $E[X_T | T < \infty] \le E[X_0]$ and $cP(\sup X_n \ge c) \le E[X_0]$

Symmetric Random Walk / Prove $S = \inf\{n : X_n = 7\}$ and $T = 10^{12} \wedge S$ are $\{\mathscr F_n^Y\}$-stopping times.

Symmetric Random Walk / Find $E[X_S]$ and $E[X_T]$

Asymmetric Random Walk / Prove $E[X_{T \wedge n}] = (p-q)E[T \wedge n]$

Convergence result of a UI martingale

Asymmetric Random Walk / Prove $E[T] = \frac{b}{p-q}$ / How do I use hint?

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