Question

Describe all martingales that only take values in $\{−1, 0, 1\}$.

score 88 · Answer 1 · 2020-06-03 13:24:24

88

Views

Describe all martingales that only take values in $\{−1, 0, 1\}$.

Published on 03 Jun 2020 - 13:24

score 72 · Answer 2 · 2020-06-03 14:09:55

72

Views

$L^p$ Boundedness of a martingale

Published on 03 Jun 2020 - 14:09

score 131 · Answer 3 · 2020-06-03 14:53:06

131

Views

Quadratic variation of true martingale

Published on 03 Jun 2020 - 14:53

score 385 · Answer 4 · 2020-06-03 15:40:43

385

Views

Show that a L2 martingale with stationary, independent increments has a certain quadratic variation

Published on 03 Jun 2020 - 15:40

score 51 · Answer 5 · 2026-03-29 12:03:37

51

Views

Counterexample for continuous time sub-martingale convergence

Published on 29 Mar 2026 - 12:03

score 210 · Answer 6 · 2026-03-26 06:18:47

210

Views

Does the Martingale Representation theorem hold both ways?

Published on 26 Mar 2026 - 6:18

score 447 · Answer 7 · 2020-06-08 16:25:14

447

Views

How to show that $Y$(martingale transform) has equal $L_2$ norm to $X$(martingale or supermartingale)?

Published on 08 Jun 2020 - 16:25

score 181 · Answer 8 · 2026-03-26 06:22:18

181

Views

Describe all martingales $(X_n)_{n\in\mathbb{N}}$, such that $X_n\in\{-1,0,1\}$ for all $n\in\mathbb{N}$ with an arbitrary sample space $\Omega$.

Published on 26 Mar 2026 - 6:22

score 159 · Answer 9 · 2020-06-09 12:36:02

159

Views

For a Wiener process $W_t$, show that $\sum_{i=1}^n h_{i-1}\big(W(t_i \wedge t) - W(t_{i-1}\wedge t)\big), \ t\ge 0$ is a martingale

Published on 09 Jun 2020 - 12:36

score 96 · Answer 10 · 2020-06-09 16:29:10

96

Views

Understanding the definition of an integral with respect to an increasing process

Published on 09 Jun 2020 - 16:29

score 53 · Answer 11 · 2020-06-10 16:16:22

53

Views

Question about stopped martingales

Published on 10 Jun 2020 - 16:16

score 111 · Answer 12 · 2026-03-27 16:27:35

111

Views

The probability that a killed random walk on $[-N,N]$ escapes before dying

Published on 27 Mar 2026 - 16:27

score 390 · Answer 13 · 2026-03-26 12:35:28

390

Views

Martingales, martingale transform, $L_2$ norm and $\textbf{Itô′s isometry}$.

Published on 26 Mar 2026 - 12:35

score 211 · Answer 14 · 2020-06-11 02:40:36

211

Views

Independence of a random variable with respect to a filtration

Published on 11 Jun 2020 - 2:40

score 79 · Answer 15 · 2026-03-27 17:57:31

79

Views

If $M$ is a martingale, show that $X_t = M_t − kt^2$ is a supermartingale iff $k$ is non-negative.

Published on 27 Mar 2026 - 17:57

List Question

Describe all martingales that only take values in $\{−1, 0, 1\}$.

$L^p$ Boundedness of a martingale

Quadratic variation of true martingale

Show that a L2 martingale with stationary, independent increments has a certain quadratic variation

Counterexample for continuous time sub-martingale convergence

Does the Martingale Representation theorem hold both ways?

How to show that $Y$(martingale transform) has equal $L_2$ norm to $X$(martingale or supermartingale)?

Describe all martingales $(X_n)_{n\in\mathbb{N}}$, such that $X_n\in\{-1,0,1\}$ for all $n\in\mathbb{N}$ with an arbitrary sample space $\Omega$.

For a Wiener process $W_t$, show that $\sum_{i=1}^n h_{i-1}\big(W(t_i \wedge t) - W(t_{i-1}\wedge t)\big), \ t\ge 0$ is a martingale

Understanding the definition of an integral with respect to an increasing process

Question about stopped martingales

The probability that a killed random walk on $[-N,N]$ escapes before dying

Martingales, martingale transform, $L_2$ norm and $\textbf{Itô′s isometry}$.

Independence of a random variable with respect to a filtration

If $M$ is a martingale, show that $X_t = M_t − kt^2$ is a supermartingale iff $k$ is non-negative.

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