Question

How to prove that the first hitting time is measurable?

score 385 · Answer 1 · 2020-02-09 17:25:28

385

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How to prove that the first hitting time is measurable?

Published on 09 Feb 2020 - 17:25

score 47 · Answer 2 · 2020-02-09 23:44:44

47

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If $T_{1} \le T_{2}$ are stopping times, then $\mathcal{F}_{T_{1}} \subseteq \mathcal{F}_{T_{2}}$

Published on 09 Feb 2020 - 23:44

score 615 · Answer 3 · 2026-03-26 03:00:53

615

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Doob's Decomposition Theorem and Uniform Integrability

Published on 26 Mar 2026 - 3:00

score 91 · Answer 4 · 2020-02-10 22:24:36

91

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How can $\mathcal{F}_{T}$ be a $\sigma$-algebra in this context of stopping time?

Published on 10 Feb 2020 - 22:24

score 47 · Answer 5 · 2020-02-11 00:12:30

47

Views

If $(X_{n})_{n \in \mathbb N}$ is a sub-martingale and $T$ a stopping time. Then $(X_{n \wedge T})_{n \in \mathbb N}$ is also a sub-martingale

Published on 11 Feb 2020 - 0:12

score 147 · Answer 6 · 2020-02-11 00:38:13

147

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$(X_{S}, X_{T})$ is a sub-martingale with respect to the filtration $(\mathcal{F}_{S}, \mathcal{F}_{T})$

Published on 11 Feb 2020 - 0:38

score 71 · Answer 7 · 2020-02-11 15:58:30

71

Views

are $T_{b-a}$ and $T_b - T_a$ equal in distribution?

Published on 11 Feb 2020 - 15:58

score 940 · Answer 8 · 2020-02-12 15:21:49

940

Views

How many normal distribution random numbers' sum exceeds $r$?

Published on 12 Feb 2020 - 15:21

score 347 · Answer 9 · 2020-02-12 23:41:15

347

Views

What does it mean by "bounded sub-martingale"?

Published on 12 Feb 2020 - 23:41

score 48 · Answer 10 · 2020-02-13 15:06:42

48

Views

How the authors conclude ${Y_{S}} =\phi_{N}\left({X_{S}}\right)$ in the proof of Optional Sampling Theorem?

Published on 13 Feb 2020 - 15:06

score 55 · Answer 11 · 2020-02-13 22:14:30

55

Views

Optional Sampling Theorem for non-positive sub-martingale

Published on 13 Feb 2020 - 22:14

score 64 · Answer 12 · 2026-02-23 10:06:32

64

Views

Optimal Stopping - Reference Request

Published on 23 Feb 2026 - 10:06

score 502 · Answer 13 · 2020-02-16 16:57:01

502

Views

Verification of the variance of the hitting time of an asymmetric random walk

Published on 16 Feb 2020 - 16:57

score 25 · Answer 14 · 2026-03-26 03:01:29

25

Views

$E\left[Y|F^X_T\right]=E[Y|X_T]$? Reducing the conditional stopped sigma algebra in a natrual filtration setting.

Published on 26 Mar 2026 - 3:01

score 82 · Answer 15 · 2026-03-26 04:33:02

82

Views

Independence of increments with stopping times in Levy processes

Published on 26 Mar 2026 - 4:33

List Question

How to prove that the first hitting time is measurable?

If $T_{1} \le T_{2}$ are stopping times, then $\mathcal{F}_{T_{1}} \subseteq \mathcal{F}_{T_{2}}$

Doob's Decomposition Theorem and Uniform Integrability

How can $\mathcal{F}_{T}$ be a $\sigma$-algebra in this context of stopping time?

If $(X_{n})_{n \in \mathbb N}$ is a sub-martingale and $T$ a stopping time. Then $(X_{n \wedge T})_{n \in \mathbb N}$ is also a sub-martingale

$(X_{S}, X_{T})$ is a sub-martingale with respect to the filtration $(\mathcal{F}_{S}, \mathcal{F}_{T})$

are $T_{b-a}$ and $T_b - T_a$ equal in distribution?

How many normal distribution random numbers' sum exceeds $r$?

What does it mean by "bounded sub-martingale"?

How the authors conclude ${Y_{S}} =\phi_{N}\left({X_{S}}\right)$ in the proof of Optional Sampling Theorem?

Optional Sampling Theorem for non-positive sub-martingale

Optimal Stopping - Reference Request

Verification of the variance of the hitting time of an asymmetric random walk

$E\left[Y|F^X_T\right]=E[Y|X_T]$? Reducing the conditional stopped sigma algebra in a natrual filtration setting.

Independence of increments with stopping times in Levy processes

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