Question

Missing Step Showing That $M_t = \exp(\alpha B_t - \alpha^2 t/2)$ doesn't converge to $0$ in $L^1$ norm.

score 90 · Answer 1 · 2021-02-08 18:55:35

90

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Missing Step Showing That $M_t = \exp(\alpha B_t - \alpha^2 t/2)$ doesn't converge to $0$ in $L^1$ norm.

Published on 08 Feb 2021 - 18:55

score 282 · Answer 2 · 2026-04-11 01:01:42

282

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Dice game - expected termination time via martingale method

Published on 11 Apr 2026 - 1:01

score 530 · Answer 3 · 2021-02-09 14:38:50

530

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Reference for Exercise 5.3.1 in [Probability: Theory and Examples, 4th edition, Durrett, 2010]

Published on 09 Feb 2021 - 14:38

score 364 · Answer 4 · 2026-02-23 22:22:15

364

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Strong law of large numbers - Continuous martingales - Reference request

Published on 23 Feb 2026 - 22:22

score 129 · Answer 5 · 2026-04-11 12:49:54

129

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Relationship between martingale and conditional expectation

Published on 11 Apr 2026 - 12:49

score 217 · Answer 6 · 2026-04-09 18:35:58

217

Views

Expectation of positive supermartingale.

Published on 09 Apr 2026 - 18:35

score 174 · Answer 7 · 2026-04-05 16:18:18

174

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Number of doublings in a bounded submartingale

Published on 05 Apr 2026 - 16:18

score 52 · Answer 8 · 2026-04-11 04:59:16

52

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How to calculate the quadratic variation of this martingale.

Published on 11 Apr 2026 - 4:59

score 120 · Answer 9 · 2026-04-06 16:20:23

120

Views

Alternative proof of generalized Borel-Cantelli without the use of the finite increment martingale limit property

Published on 06 Apr 2026 - 16:20

score 79 · Answer 10 · 2026-04-11 21:34:45

79

Views

Intuition of martingale compensators

Published on 11 Apr 2026 - 21:34

score 60 · Answer 11 · 2021-02-17 23:26:34

60

Views

Is log(1+$M^{2}$) a maringale/submaringale/supermartingale, given that $M$ is a martingale?

Published on 17 Feb 2021 - 23:26

score 55 · Answer 12 · 2026-04-03 00:17:05

55

Views

Doobs Optional sampling theorem condition escapes intuition

Published on 03 Apr 2026 - 0:17

score 1.3k · Answer 13 · 2026-04-03 00:19:10

1.3k

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Stopping times: bounded vs unbounded, example for a bounded stopping time

Published on 03 Apr 2026 - 0:19

score 222 · Answer 14 · 2021-02-21 11:57:56

222

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Need continuous time martingales be predictable?

Published on 21 Feb 2021 - 11:57

score 458 · Answer 15 · 2021-02-23 11:13:28

458

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If $(X_n)_{n\in \mathbb{N}}$ is a martingale s.t. $\sup_n E[|X_n|]\leq M < \infty$, then $\sum_{n\geq 2}(X_n-X_{n-1})^2<\infty$ almost surely.

Published on 23 Feb 2021 - 11:13

List Question

Missing Step Showing That $M_t = \exp(\alpha B_t - \alpha^2 t/2)$ doesn't converge to $0$ in $L^1$ norm.

Dice game - expected termination time via martingale method

Reference for Exercise 5.3.1 in [Probability: Theory and Examples, 4th edition, Durrett, 2010]

Strong law of large numbers - Continuous martingales - Reference request

Relationship between martingale and conditional expectation

Expectation of positive supermartingale.

Number of doublings in a bounded submartingale

How to calculate the quadratic variation of this martingale.

Alternative proof of generalized Borel-Cantelli without the use of the finite increment martingale limit property

Intuition of martingale compensators

Is log(1+$M^{2}$) a maringale/submaringale/supermartingale, given that $M$ is a martingale?

Doobs Optional sampling theorem condition escapes intuition

Stopping times: bounded vs unbounded, example for a bounded stopping time

Need continuous time martingales be predictable?

If $(X_n)_{n\in \mathbb{N}}$ is a martingale s.t. $\sup_n E[|X_n|]\leq M < \infty$, then $\sum_{n\geq 2}(X_n-X_{n-1})^2<\infty$ almost surely.

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