List questions from stopping-times

Published on 30 May 2022 - 17:19

51

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How can we characterize $\tau\le t$ for $\tau:=\{t\ge0:x(t)\in B\}$?

Published on 07 Jun 2022 - 17:46

37

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Is $\tau:=\inf\left\{t\ge0:\int_0^tc(X_s)\:{\rm d}s\ge\xi\right\}$ a stopping time?

Published on 09 Jun 2022 - 8:34

32

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inconsistent definitions of the $\sigma$-algebra of the $\tau$-past

Published on 11 Jun 2022 - 7:39

31

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How can we show $\operatorname E\left[Y_\tau;t\ge\tau\mid\tau=s\right]=1_{\{\:t\:\ge\:s\:\}}\operatorname E\left[Y_s\right]$?

Published on 13 Jun 2022 - 5:38

131

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Optimal Stopping Time

Published on 24 Feb 2026 - 13:24

76

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If $f$ is $\mathcal F_{\tau-}$-measurable, is $1_{\{\:s\:<\:\tau\:\}}f$ is $\mathcal F_s$-measurable for all $s\ge0$?

Published on 17 Jun 2022 - 17:37

343

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Why is a constant always a stopping time?

Published on 18 Jun 2022 - 15:32

186

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Stopping Time: Diffrences in discrete and continuous time

Published on 27 Mar 2026 - 9:37

70

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Distribution of difference of first hitting times of Brownian motion

Published on 19 Jun 2022 - 18:53

64

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How do we show $\operatorname E\left[X_\tau\mid\tau=t\right]=\operatorname E\left[X_t\mid\tau=t\right]$?

Published on 28 Jun 2022 - 17:17

270

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Random walk with a killing probability

Published on 28 Jun 2022 - 23:49

190

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Calculating $\mathbb{E}[N]$ for $N = \displaystyle \min_{n\in \mathbb{N}}\Big\{\sum_{i=1}^{n}{X_i\geq5000\Big\}}$, using Wald's lemma

Published on 01 Jul 2022 - 9:24

40

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Can we show $A\cap\{\tau=\infty\}\in\mathcal F_{\tau-}$?

Published on 12 Jul 2022 - 7:54

45

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Proof of the existence of minimal stopping times

Published on 26 Feb 2026 - 12:36

List Question

martingale, stopping times

How can we characterize $\tau\le t$ for $\tau:=\{t\ge0:x(t)\in B\}$?

Is $\tau:=\inf\left\{t\ge0:\int_0^tc(X_s)\:{\rm d}s\ge\xi\right\}$ a stopping time?

inconsistent definitions of the $\sigma$-algebra of the $\tau$-past

How can we show $\operatorname E\left[Y_\tau;t\ge\tau\mid\tau=s\right]=1_{\{\:t\:\ge\:s\:\}}\operatorname E\left[Y_s\right]$?

Optimal Stopping Time

If $f$ is $\mathcal F_{\tau-}$-measurable, is $1_{\{\:s\:<\:\tau\:\}}f$ is $\mathcal F_s$-measurable for all $s\ge0$?

Why is a constant always a stopping time?

Stopping Time: Diffrences in discrete and continuous time

Distribution of difference of first hitting times of Brownian motion

How do we show $\operatorname E\left[X_\tau\mid\tau=t\right]=\operatorname E\left[X_t\mid\tau=t\right]$?

Random walk with a killing probability

Calculating $\mathbb{E}[N]$ for $N = \displaystyle \min_{n\in \mathbb{N}}\Big\{\sum_{i=1}^{n}{X_i\geq5000\Big\}}$, using Wald's lemma

Can we show $A\cap\{\tau=\infty\}\in\mathcal F_{\tau-}$?

Proof of the existence of minimal stopping times

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