List questions from martingales

Published on 26 Mar 2026 - 17:53

42

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Prove $\frac{1}{2}E[T_x] \le \frac{x}{E[\min(X_1,x)]} \le E[T_x]$ : stopping time

Published on 23 Oct 2019 - 20:45

74

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A continuous process s.t. $\mathbb E[X_{t+1}\mid \mathcal F_t]=X_t$ is a martingale?

Published on 24 Oct 2019 - 15:29

36

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Distribution of a limit random variable $X_{\infty}$

Published on 26 Oct 2019 - 14:10

97

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$\{S_n\}_n$ is a Cauchy sequence in $L^2$

Published on 26 Oct 2019 - 17:42

595

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Martingale: show switching of two supermartingales with a stopping time is also a supermartingale

Published on 27 Oct 2019 - 2:09

111

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When doob martingale is continuous

Published on 30 Oct 2019 - 16:08

335

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Compare Doob décomposition for stochastic process $(X_t)_{t\geq 0}$ and $(X_n)_{n\in\mathbb N}$

Published on 23 Feb 2026 - 4:40

56

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$EM_T=1 \implies M_t$ is a martingale

Published on 30 Oct 2019 - 20:33

264

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Completeness of continuous $L^2$-martingales

Published on 26 Mar 2026 - 6:27

61

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Supermartingale with bdd increment and positive variance before $\tau$ satisfies $P_k(\tau >u) \leq \frac{4k}{\sigma \sqrt{u}}$ for large $u$.

Published on 26 Mar 2026 - 17:53

53

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E[$X_n$] of submartingale is increasing

Published on 01 Nov 2019 - 18:33

71

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Probability of Convergence of Stochastic Process to $1$

Published on 02 Nov 2019 - 3:16

117

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Optional stopping theorem for backwards martingales

Published on 02 Nov 2019 - 14:57

479

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1-Player Fair Gambler's Ruin

Published on 02 Nov 2019 - 15:38

List Question

Implication of a positive endvalue of a martingale $(M_t)_{t\in [0,T]}$

Prove $\frac{1}{2}E[T_x] \le \frac{x}{E[\min(X_1,x)]} \le E[T_x]$ : stopping time

A continuous process s.t. $\mathbb E[X_{t+1}\mid \mathcal F_t]=X_t$ is a martingale?

Distribution of a limit random variable $X_{\infty}$

$\{S_n\}_n$ is a Cauchy sequence in $L^2$

Martingale: show switching of two supermartingales with a stopping time is also a supermartingale

When doob martingale is continuous

Compare Doob décomposition for stochastic process $(X_t)_{t\geq 0}$ and $(X_n)_{n\in\mathbb N}$

$EM_T=1 \implies M_t$ is a martingale

Completeness of continuous $L^2$-martingales

Supermartingale with bdd increment and positive variance before $\tau$ satisfies $P_k(\tau >u) \leq \frac{4k}{\sigma \sqrt{u}}$ for large $u$.

E[$X_n$] of submartingale is increasing

Probability of Convergence of Stochastic Process to $1$

Optional stopping theorem for backwards martingales

1-Player Fair Gambler's Ruin

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