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Questions about proving the statement: $\tau(\omega)$ is a stopping time, iff $\{ \tau(\omega) < t\}$ $\in \mathcal{F}_t$, for all $t \geq 0$.

score 129 · Answer 1 · 2026-03-26 06:23:09

129

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Questions about proving the statement: $\tau(\omega)$ is a stopping time, iff $\{ \tau(\omega) < t\}$ $\in \mathcal{F}_t$, for all $t \geq 0$.

Published on 26 Mar 2026 - 6:23

score 181 · Answer 2 · 2020-07-10 17:29:13

181

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Prove that $P(\tau<\infty)=1$ and find the distribution of $X_\tau$

Published on 10 Jul 2020 - 17:29

score 364 · Answer 3 · 2020-07-14 14:10:00

364

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Variance of the exponential hitting time of a random walk

Published on 14 Jul 2020 - 14:10

score 805 · Answer 4 · 2020-07-23 13:08:31

805

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Intuition behind Doob's Optional Stopping theorem

Published on 23 Jul 2020 - 13:08

score 58 · Answer 5 · 2026-03-26 07:57:20

58

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Optimal rule for multiple stopping times for defect finding

Published on 26 Mar 2026 - 7:57

score 47 · Answer 6 · 2016-07-07 21:58:07

47

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Comparison of stopped sub- and supermartingales when the future is discounted

Published on 07 Jul 2016 - 21:58

score 187 · Answer 7 · 2016-07-08 07:45:19

187

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The hitting time $T-\tau^{l}$ has the same distribution as $\min\{\tau^{f},T\}$ regarding an Poisson Process.

Published on 08 Jul 2016 - 7:45

score 272 · Answer 8 · 2016-07-12 08:35:27

272

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Predictable stopping time

Published on 12 Jul 2016 - 8:35

score 68 · Answer 9 · 2016-07-13 19:42:41

68

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How to show that $S_k = \inf \{t \geq 0 | \|X(t)\| \geq k \} \to \infty$ as $k \to \infty$ a.s.

Published on 13 Jul 2016 - 19:42

score 2.4k · Answer 10 · 2016-07-21 17:42:11

2.4k

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Expected hitting time of Ornstein-Uhlenbeck process

Published on 21 Jul 2016 - 17:42

score 379 · Answer 11 · 2026-03-26 09:38:45

379

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A proof by René Schilling that a continuous Lévy process is integrable

Published on 26 Mar 2026 - 9:38

score 78 · Answer 12 · 2016-07-31 15:18:59

78

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Stopping time and Successive passage of barriers for a real Brownian motion

Published on 31 Jul 2016 - 15:18

score 658 · Answer 13 · 2016-08-02 10:40:36

658

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Stopping time and open/closed sets

Published on 02 Aug 2016 - 10:40

score 196 · Answer 14 · 2026-02-23 06:39:38

196

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Trouble understanding construction of quadratic variation of martingale

Published on 23 Feb 2026 - 6:39

score 1.1k · Answer 15 · 2016-08-09 05:04:41

1.1k

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Expected position of a random walk with a biased coin directly after two consecutive heads are observed

Published on 09 Aug 2016 - 5:04

List Question

Questions about proving the statement: $\tau(\omega)$ is a stopping time, iff $\{ \tau(\omega) < t\}$ $\in \mathcal{F}_t$, for all $t \geq 0$.

Prove that $P(\tau<\infty)=1$ and find the distribution of $X_\tau$

Variance of the exponential hitting time of a random walk

Intuition behind Doob's Optional Stopping theorem

Optimal rule for multiple stopping times for defect finding

Comparison of stopped sub- and supermartingales when the future is discounted

The hitting time $T-\tau^{l}$ has the same distribution as $\min\{\tau^{f},T\}$ regarding an Poisson Process.

Predictable stopping time

How to show that $S_k = \inf \{t \geq 0 | \|X(t)\| \geq k \} \to \infty$ as $k \to \infty$ a.s.

Expected hitting time of Ornstein-Uhlenbeck process

A proof by René Schilling that a continuous Lévy process is integrable

Stopping time and Successive passage of barriers for a real Brownian motion

Stopping time and open/closed sets

Trouble understanding construction of quadratic variation of martingale

Expected position of a random walk with a biased coin directly after two consecutive heads are observed

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