Question

Prove result for a bounded continuous martingale with finite variation.

score 86 · Answer 1 · 2020-10-22 22:47:15

86

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Prove result for a bounded continuous martingale with finite variation.

Published on 22 Oct 2020 - 22:47

score 70 · Answer 2 · 2026-04-09 02:13:05

70

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Question about the expectation of martingales

Published on 09 Apr 2026 - 2:13

score 27 · Answer 3 · 2020-10-23 16:33:52

27

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Clarification on when is $X_T$ integrable (martingale theory)

Published on 23 Oct 2020 - 16:33

score 87 · Answer 4 · 2020-10-23 17:13:00

87

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Is $(M_n^5)_{n \in \mathbb{N}_0}$ a martingale, given that both $(M_n)_{n \in \mathbb{N}_0}$ and $(M_n^2 )_{n \in \mathbb{N}_0}$are martingales?

Published on 23 Oct 2020 - 17:13

score 54 · Answer 5 · 2026-04-08 17:37:22

54

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Show that the following 2 times are equal in distribution.

Published on 08 Apr 2026 - 17:37

score 40 · Answer 6 · 2026-04-09 01:48:15

40

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Is it a submartingale?

Published on 09 Apr 2026 - 1:48

score 71 · Answer 7 · 2020-10-26 18:42:53

71

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For what exactly we need that the submartingale is a finite sequence in theorem 6.7.3 of Ash's book?

Published on 26 Oct 2020 - 18:42

score 323 · Answer 8 · 2026-04-02 17:44:30

323

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For a Brownian motion $B(t)$, show $0=\mathbb E[ B(\tau)]$ where $\tau := \max \{\tau_a, \tau_b\}$ is the latter hitting time of the levels $a<0<b$.

Published on 02 Apr 2026 - 17:44

score 43 · Answer 9 · 2026-04-02 17:42:51

43

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$\mathbb{E}[M_{a}]\geq \mathbb{E}[M_{b}]$ with $a,b$ limited stopping times and $M$ sub-martingale

Published on 02 Apr 2026 - 17:42

score 136 · Answer 10 · 2020-10-27 16:33:26

136

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Show that $M_n = \sum_{i=1}^n \alpha_k(X_k -X_{k-1})$ is a square integrable martingale w.r.t. $\{F_n, \ n\in \mathbb{N}\}$.

Published on 27 Oct 2020 - 16:33

score 109 · Answer 11 · 2026-04-09 13:28:33

109

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Probability puzzle for a fair die

Published on 09 Apr 2026 - 13:28

score 90 · Answer 12 · 2026-04-09 11:22:38

90

Views

Regarding the Maximum of Two Stopping Times

Published on 09 Apr 2026 - 11:22

score 208 · Answer 13 · 2026-02-23 16:57:58

208

Views

Using various inequalities to prove this martingale inequality?

Published on 23 Feb 2026 - 16:57

score 120 · Answer 14 · 2026-03-27 04:21:57

120

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If $(X_k)_{k\in\mathbb N}$, show that $\sum_{k=1}^n(X_k-\text E[X_k])$ converges almost surely as $n\to\infty$

Published on 27 Mar 2026 - 4:21

score 472 · Answer 15 · 2020-10-31 08:55:58

472

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Convergence of quadratic variations

Published on 31 Oct 2020 - 8:55

List Question

Prove result for a bounded continuous martingale with finite variation.

Question about the expectation of martingales

Clarification on when is $X_T$ integrable (martingale theory)

Is $(M_n^5)_{n \in \mathbb{N}_0}$ a martingale, given that both $(M_n)_{n \in \mathbb{N}_0}$ and $(M_n^2 )_{n \in \mathbb{N}_0}$are martingales?

Show that the following 2 times are equal in distribution.

Is it a submartingale?

For what exactly we need that the submartingale is a finite sequence in theorem 6.7.3 of Ash's book?

For a Brownian motion $B(t)$, show $0=\mathbb E[ B(\tau)]$ where $\tau := \max \{\tau_a, \tau_b\}$ is the latter hitting time of the levels $a<0<b$.

$\mathbb{E}[M_{a}]\geq \mathbb{E}[M_{b}]$ with $a,b$ limited stopping times and $M$ sub-martingale

Show that $M_n = \sum_{i=1}^n \alpha_k(X_k -X_{k-1})$ is a square integrable martingale w.r.t. $\{F_n, \ n\in \mathbb{N}\}$.

Probability puzzle for a fair die

Regarding the Maximum of Two Stopping Times

Using various inequalities to prove this martingale inequality?

If $(X_k)_{k\in\mathbb N}$, show that $\sum_{k=1}^n(X_k-\text E[X_k])$ converges almost surely as $n\to\infty$

Convergence of quadratic variations

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