Question

How can I show that $T(\omega) = T(\overline{\omega})$ when $X_{t}(\omega)=X_{t}(\overline{\omega})$ for all $t \in [0,T(\omega)]\cap [0,\infty)$

score 83 · Answer 1 · 2020-11-24 20:55:00

83

Views

How can I show that $T(\omega) = T(\overline{\omega})$ when $X_{t}(\omega)=X_{t}(\overline{\omega})$ for all $t \in [0,T(\omega)]\cap [0,\infty)$

Published on 24 Nov 2020 - 20:55

score 299 · Answer 2 · 2026-02-23 16:56:58

299

Views

Local times and quadratic variation

Published on 23 Feb 2026 - 16:56

score 45 · Answer 3 · 2020-11-29 12:17:33

45

Views

$L = \begin{cases} M & \text{on }\; A\\ N & \text{on} \; A^c \end{cases}$ is a stopping time

Published on 29 Nov 2020 - 12:17

score 124 · Answer 4 · 2020-11-29 19:41:56

124

Views

If S and T are stopping times, with $S \leq T$, X is a continuous stochastic process, if T reduces X, does S reduce X?

Published on 29 Nov 2020 - 19:41

score 343 · Answer 5 · 2026-03-29 05:49:44

343

Views

Is this stopping time finite a.s ? bounded?

Published on 29 Mar 2026 - 5:49

score 140 · Answer 6 · 2020-11-30 16:43:02

140

Views

Intuition for $\mathbb{E}[\tau]=\infty$ but $\mathbb{P}(\tau = \infty)=0$

Published on 30 Nov 2020 - 16:43

score 215 · Answer 7 · 2020-12-02 13:49:07

215

Views

Laplace transform of time until absorption of Brownian motion

Published on 02 Dec 2020 - 13:49

score 184 · Answer 8 · 2026-03-27 09:20:32

184

Views

Finding the stopping time in casino game

Published on 27 Mar 2026 - 9:20

score 47 · Answer 9 · 2020-12-10 07:04:22

47

Views

A problem regarding the stopped $\sigma$-field

Published on 10 Dec 2020 - 7:04

score 190 · Answer 10 · 2026-03-27 04:16:37

190

Views

stopped UI discrete time martingale is UI

Published on 27 Mar 2026 - 4:16

score 131 · Answer 11 · 2020-12-10 19:58:05

131

Views

Compute the probability that $\Pr(\tau<\infty)$.

Published on 10 Dec 2020 - 19:58

score 403 · Answer 12 · 2026-03-26 21:13:57

403

Views

In the definition of a Stopping Time, how important are the conditions on the Filtration being complete and right-continuous?

Published on 26 Mar 2026 - 21:13

score 26 · Answer 13 · 2020-12-11 17:33:54

26

Views

A stochastic Process where $X_{T_A}\not \in A$. Must it always be in $\bar A$?

Published on 11 Dec 2020 - 17:33

score 66 · Answer 14 · 2026-03-27 13:39:51

66

Views

Applying the Optional Stopping Theorem to martingale with no upper bound?

Published on 27 Mar 2026 - 13:39

score 220 · Answer 15 · 2026-03-27 04:15:03

220

Views

Integrable submartingale

Published on 27 Mar 2026 - 4:15

List Question

How can I show that $T(\omega) = T(\overline{\omega})$ when $X_{t}(\omega)=X_{t}(\overline{\omega})$ for all $t \in [0,T(\omega)]\cap [0,\infty)$

Local times and quadratic variation

$L = \begin{cases} M & \text{on }\; A\\ N & \text{on} \; A^c \end{cases}$ is a stopping time

If S and T are stopping times, with $S \leq T$, X is a continuous stochastic process, if T reduces X, does S reduce X?

Is this stopping time finite a.s ? bounded?

Intuition for $\mathbb{E}[\tau]=\infty$ but $\mathbb{P}(\tau = \infty)=0$

Laplace transform of time until absorption of Brownian motion

Finding the stopping time in casino game

A problem regarding the stopped $\sigma$-field

stopped UI discrete time martingale is UI

Compute the probability that $\Pr(\tau<\infty)$.

In the definition of a Stopping Time, how important are the conditions on the Filtration being complete and right-continuous?

A stochastic Process where $X_{T_A}\not \in A$. Must it always be in $\bar A$?

Applying the Optional Stopping Theorem to martingale with no upper bound?

Integrable submartingale

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