List questions from martingales

Published on 14 Jun 2021 - 14:53

178

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stochastic exponential of continuous local martingale is local martingale

Published on 11 Apr 2026 - 17:17

118

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$M_t = \frac{1}{\sqrt{T_1}} \mathbb{1} (T_1 \leq t) - 2 \sqrt{T_1 \wedge t}, t\geq 0$ is a martingale

Published on 01 Apr 2026 - 2:30

157

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If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $E[X\mid\mathcal{F}_k]$ converges to $E[X\mid\mathcal{W}]$

Published on 24 Jun 2021 - 1:41

141

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Looking for a maximal inequality for supermartingales

Published on 24 Jun 2021 - 14:46

366

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Let $W$ be a standard Brownian motion, compute the stochastic integral $\int_0^t s W_s^2dW_s$. Why should I use $f(t,x)=tx^3/3$?

Published on 07 Apr 2026 - 6:16

115

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On Doob's Upcrossing Inequality supermartingales/submartingales' switch

Published on 06 Apr 2026 - 14:40

150

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Understanding Kolmogorov's inequality for submartingales

Published on 12 Apr 2026 - 7:42

352

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Show that $Z_n=\frac{X_n}{m^n}$ is a martingale

Published on 02 Jul 2021 - 6:15

73

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CEV process is a strict supermartingale

Published on 10 Apr 2026 - 8:55

70

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Computing a conditional probability using a martingle

Published on 10 Apr 2026 - 7:47

247

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Application of Doob's maximal inequality

Published on 07 Apr 2026 - 6:14

474

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Central Limit Theorem & Random Walks

Published on 06 Apr 2026 - 18:57

579

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Bachelier model option pricing

Published on 11 Apr 2026 - 20:32

342

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$e^{X_t}$ is martingale using Ito's Formula

Published on 12 Apr 2026 - 5:17

List Question

Conditional variance of a Martingale Difference Sequence

stochastic exponential of continuous local martingale is local martingale

$M_t = \frac{1}{\sqrt{T_1}} \mathbb{1} (T_1 \leq t) - 2 \sqrt{T_1 \wedge t}, t\geq 0$ is a martingale

If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $E[X\mid\mathcal{F}_k]$ converges to $E[X\mid\mathcal{W}]$

Looking for a maximal inequality for supermartingales

Let $W$ be a standard Brownian motion, compute the stochastic integral $\int_0^t s W_s^2dW_s$. Why should I use $f(t,x)=tx^3/3$?

On Doob's Upcrossing Inequality supermartingales/submartingales' switch

Understanding Kolmogorov's inequality for submartingales

Show that $Z_n=\frac{X_n}{m^n}$ is a martingale

CEV process is a strict supermartingale

Computing a conditional probability using a martingle

Application of Doob's maximal inequality

Central Limit Theorem & Random Walks

Bachelier model option pricing

$e^{X_t}$ is martingale using Ito's Formula

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