Question

Show that $\mathcal{E}_t(M)$ is a continuous martingale bounded in $L^2$

score 43 · Answer 1 · 2019-11-27 21:22:07

43

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Show that $\mathcal{E}_t(M)$ is a continuous martingale bounded in $L^2$

Published on 27 Nov 2019 - 21:22

score 657 · Answer 2 · 2019-11-28 02:41:11

657

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Martingale convergence (Durrett probability 4th edition 5.2.11)

Published on 28 Nov 2019 - 2:41

score 304 · Answer 3 · 2019-11-28 02:49:00

304

Views

Lipschitz continuity for a martingale (Durrett probability 4th edition 5.5.3)

Published on 28 Nov 2019 - 2:49

score 323 · Answer 4 · 2026-02-23 06:24:13

323

Views

Proving $X_t$ is a Martingale with respect to natural filtration

Published on 23 Feb 2026 - 6:24

score 57 · Answer 5 · 2019-11-29 15:45:23

57

Views

Show $\sum_{n \geq 1}\mathbb{1}_{A_n}(\omega) = \infty$ iff $\sum_{n \geq 1} \mathbb{E}[\mathbb{1}_{A_n}|\mathcal{F}_{n-1}](\omega) = \infty$

Published on 29 Nov 2019 - 15:45

score 61 · Answer 6 · 2019-11-30 10:38:24

61

Views

Given $0\leq s <t,$ why is $E[(W(t)-W(s))^2 |F(s)] = E[(W(t)-W(s))^2]?$

Published on 30 Nov 2019 - 10:38

score 41 · Answer 7 · 2019-12-02 11:57:29

41

Views

Convergence of martingales

Published on 02 Dec 2019 - 11:57

score 68 · Answer 8 · 2026-03-26 17:53:37

68

Views

Stopping time and martingale of $ \min \left\{ n \geq 1 : X_n = Y_n \right\}$

Published on 26 Mar 2026 - 17:53

score 32 · Answer 9 · 2019-12-03 09:41:50

32

Views

Optional Sampling Theorem in the Continuous Case

Published on 03 Dec 2019 - 9:41

score 52 · Answer 10 · 2026-03-26 17:53:50

52

Views

Stopping time of $ \min \left\{ n \geq 1 : X_n = Y_n \right\}$

Published on 26 Mar 2026 - 17:53

score 165 · Answer 11 · 2019-12-03 21:31:39

165

Views

The real and imaginary parts of $X_t = \exp[iuN_t - \lambda t(e^{iu}-1)]; \; 0 \le t < \infty$ are martingales

Published on 03 Dec 2019 - 21:31

score 198 · Answer 12 · 2019-12-04 03:32:32

198

Views

Problem 1.3.24 (ii) Karatzas and Shreve $E[X_{T \wedge t}|\mathscr{F}_S]\ge X_{S \wedge t}$ for $S \le T$ and submartingale $X$.

Published on 04 Dec 2019 - 3:32

score 200 · Answer 13 · 2019-12-04 04:04:52

200

Views

Karatzas and Shreve Problem 1.3.24(i). $X_{T \wedge t}, \mathscr{F}_t$ is a submartingale.

Published on 04 Dec 2019 - 4:04

score 3.1k · Answer 14 · 2026-03-26 03:00:44

3.1k

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Proving a Wiener Process is a Martingale

Published on 26 Mar 2026 - 3:00

score 139 · Answer 15 · 2026-03-27 22:11:58

139

Views

$n$-th power of stochastic exponential

Published on 27 Mar 2026 - 22:11

List Question

Show that $\mathcal{E}_t(M)$ is a continuous martingale bounded in $L^2$

Martingale convergence (Durrett probability 4th edition 5.2.11)

Lipschitz continuity for a martingale (Durrett probability 4th edition 5.5.3)

Proving $X_t$ is a Martingale with respect to natural filtration

Show $\sum_{n \geq 1}\mathbb{1}_{A_n}(\omega) = \infty$ iff $\sum_{n \geq 1} \mathbb{E}[\mathbb{1}_{A_n}|\mathcal{F}_{n-1}](\omega) = \infty$

Given $0\leq s <t,$ why is $E[(W(t)-W(s))^2 |F(s)] = E[(W(t)-W(s))^2]?$

Convergence of martingales

Stopping time and martingale of $ \min \left\{ n \geq 1 : X_n = Y_n \right\}$

Optional Sampling Theorem in the Continuous Case

Stopping time of $ \min \left\{ n \geq 1 : X_n = Y_n \right\}$

The real and imaginary parts of $X_t = \exp[iuN_t - \lambda t(e^{iu}-1)]; \; 0 \le t < \infty$ are martingales

Problem 1.3.24 (ii) Karatzas and Shreve $E[X_{T \wedge t}|\mathscr{F}_S]\ge X_{S \wedge t}$ for $S \le T$ and submartingale $X$.

Karatzas and Shreve Problem 1.3.24(i). $X_{T \wedge t}, \mathscr{F}_t$ is a submartingale.

Proving a Wiener Process is a Martingale

$n$-th power of stochastic exponential

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