Question

Maximum of Random Variables

score 70 · Answer 1 · 2017-06-12 14:53:06

70

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Maximum of Random Variables

Published on 12 Jun 2017 - 14:53

score 783 · Answer 2 · 2026-03-30 12:18:56

783

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CLT for martingale difference array

Published on 30 Mar 2026 - 12:18

score 181 · Answer 3 · 2026-03-26 22:55:21

181

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For right continuous martingales and a collection of stopping times, for each $T>0$, $\{X(T\wedge \tau):\tau \in S\}$ is uniformly integrable

Published on 26 Mar 2026 - 22:55

score 215 · Answer 4 · 2026-02-23 15:11:05

215

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Example of a random variable $X$ that is an $\mathscr{F}_t$-local martingale, but not an $\mathscr{F}_t^X$-local martingale.

Published on 23 Feb 2026 - 15:11

score 276 · Answer 5 · 2017-06-13 20:16:49

276

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Details in proof for Doob's $L^p$-inequality

Published on 13 Jun 2017 - 20:16

score 97 · Answer 6 · 2017-06-15 19:52:13

97

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Is this a metric in the space of continuous martingales?

Published on 15 Jun 2017 - 19:52

score 80 · Answer 7 · 2017-06-15 20:51:01

80

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Stopped Martingale Convergence

Published on 15 Jun 2017 - 20:51

score 159 · Answer 8 · 2026-03-31 08:01:18

159

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If $(X_t)_{t∈I}$ is a martingale and $τ$ is a stopping time with $τ≤T$, then $X_τ=\text E[X_T\mid\mathcal F_τ]$. Why does $I$ need to be countable?

Published on 31 Mar 2026 - 8:01

score 241 · Answer 9 · 2026-03-31 08:00:45

241

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If $M$ is a martingale and $σ_n↓$ and $τ_n↓τ$, then $\text E[M_{τ_n}\mid\mathcal F_{σ_n}]\xrightarrow{n→∞}\text E[M_τ\mid\mathcal F_σ]$

Published on 31 Mar 2026 - 8:00

score 1.5k · Answer 10 · 2026-02-23 15:06:45

1.5k

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Is a stopped local martingale a local martingale?

Published on 23 Feb 2026 - 15:06

score 687 · Answer 11 · 2026-03-30 06:30:45

687

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Convergence of an exponential martingale

Published on 30 Mar 2026 - 6:30

score 118 · Answer 12 · 2026-02-23 15:06:32

118

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Integrability of inverted Brownian Motion

Published on 23 Feb 2026 - 15:06

score 90 · Answer 13 · 2026-02-23 15:11:13

90

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If $M$ is a local martingale and $τ:=\inf\left\{t≥0:|M_t|≥ε\right\}$, then $\text P[[M]_∞≥δ]≤\text P[τ<∞]+\text P[[M]_τ≥δ]$

Published on 23 Feb 2026 - 15:11

score 205 · Answer 14 · 2026-03-31 22:30:42

205

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are sub-martingales correlated with the indicator function of stopping times?

Published on 31 Mar 2026 - 22:30

score 2.7k · Answer 15 · 2026-04-05 08:37:39

2.7k

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Examples of super- and sub- martingale, which is not a random walk, nor a function of such

Published on 05 Apr 2026 - 8:37

List Question

Maximum of Random Variables

CLT for martingale difference array

For right continuous martingales and a collection of stopping times, for each $T>0$, $\{X(T\wedge \tau):\tau \in S\}$ is uniformly integrable

Example of a random variable $X$ that is an $\mathscr{F}_t$-local martingale, but not an $\mathscr{F}_t^X$-local martingale.

Details in proof for Doob's $L^p$-inequality

Is this a metric in the space of continuous martingales?

Stopped Martingale Convergence

If $(X_t)_{t∈I}$ is a martingale and $τ$ is a stopping time with $τ≤T$, then $X_τ=\text E[X_T\mid\mathcal F_τ]$. Why does $I$ need to be countable?

If $M$ is a martingale and $σ_n↓$ and $τ_n↓τ$, then $\text E[M_{τ_n}\mid\mathcal F_{σ_n}]\xrightarrow{n→∞}\text E[M_τ\mid\mathcal F_σ]$

Is a stopped local martingale a local martingale?

Convergence of an exponential martingale

Integrability of inverted Brownian Motion

If $M$ is a local martingale and $τ:=\inf\left\{t≥0:|M_t|≥ε\right\}$, then $\text P[[M]_∞≥δ]≤\text P[τ<∞]+\text P[[M]_τ≥δ]$

are sub-martingales correlated with the indicator function of stopping times?

Examples of super- and sub- martingale, which is not a random walk, nor a function of such

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