List questions from martingales

Published on 18 Jan 2021 - 21:47

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How to generalize the result $E(\sum_i^N X_i)=E(X_1)E(N)$ to the case where $X_i$ are not iid?

Published on 02 Apr 2026 - 20:58

123

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Using the monotone class argument to prove martingale property

Published on 09 Apr 2026 - 10:08

88

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Set $M_t = 4B_t^2 + e^{4B_t -8t} -4t$. Find $\mathbb{E}(M_\sigma)$ for $\sigma = \inf(t \geq 0 : |B_t| = 1)$.

Published on 02 Apr 2026 - 20:57

207

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Let $B = (B_t)_{t \geq 0}$ be a standard brownian motion and $I_t = \inf_{0 \leq s \leq t} B_s$, show $F(t, B_t, I_t)$ is a martingale.

Published on 06 Apr 2026 - 16:01

347

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How can a discrete stochastic integral be used to show that $(X_n)$ submartingale, $S\le T\implies E(X_S)\le E(X_T)$

Published on 20 Jan 2021 - 10:05

128

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Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

Published on 02 Apr 2026 - 20:54

60

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non integrability of stopping time in martingales

Published on 11 Apr 2026 - 19:50

111

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Martingale with expectation

Published on 21 Jan 2021 - 2:56

85

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Product of this dependent martingales is also a martingale?

Published on 22 Jan 2021 - 15:15

271

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When is a Markov of order 1 a Martingale?

Published on 06 Apr 2026 - 5:58

156

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Conclude almost sure convergence from the expectation

Published on 11 Apr 2026 - 7:51

189

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Properties of Quadratic Covariation

Published on 11 Apr 2026 - 17:17

176

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Types of convergence of a Martingale

Published on 23 Jan 2021 - 10:21

50

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Uniform integrability and converging process

Published on 27 Mar 2026 - 4:15

List Question

Convergence in $L^1$ of martingale related to a Poisson process

How to generalize the result $E(\sum_i^N X_i)=E(X_1)E(N)$ to the case where $X_i$ are not iid?

Using the monotone class argument to prove martingale property

Set $M_t = 4B_t^2 + e^{4B_t -8t} -4t$. Find $\mathbb{E}(M_\sigma)$ for $\sigma = \inf(t \geq 0 : |B_t| = 1)$.

Let $B = (B_t)_{t \geq 0}$ be a standard brownian motion and $I_t = \inf_{0 \leq s \leq t} B_s$, show $F(t, B_t, I_t)$ is a martingale.

How can a discrete stochastic integral be used to show that $(X_n)$ submartingale, $S\le T\implies E(X_S)\le E(X_T)$

Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

non integrability of stopping time in martingales

Martingale with expectation

Product of this dependent martingales is also a martingale?

When is a Markov of order 1 a Martingale?

Conclude almost sure convergence from the expectation

Properties of Quadratic Covariation

Types of convergence of a Martingale

Uniform integrability and converging process

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