Question

Show that $(V_{n})_{n \le N}$ is a $\mathcal{F}_n$-martingale

score 31 · Answer 1 · 2020-02-09 09:38:49

31

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Show that $(V_{n})_{n \le N}$ is a $\mathcal{F}_n$-martingale

Published on 09 Feb 2020 - 9:38

score 34 · Answer 2 · 2020-02-09 12:42:35

34

Views

Show that $(M_{n})$ with $M_{n}=(X_{n}-\mathbb{E}(X_{n}))^{2}-\operatorname{Var}(X_{n})$ is a $\mathcal{F}_{n}$-martingale

Published on 09 Feb 2020 - 12:42

score 47 · Answer 3 · 2020-02-09 18:55:13

47

Views

Finding a regular process which is a martingale

Published on 09 Feb 2020 - 18:55

score 615 · Answer 4 · 2026-03-26 03:00:53

615

Views

Doob's Decomposition Theorem and Uniform Integrability

Published on 26 Mar 2026 - 3:00

score 197 · Answer 5 · 2026-03-26 08:03:28

197

Views

If $\mathbb E[\sup_{t\in [0,T]}|X_t|]<\infty$, is $(X_t)_{t\in [0,T]}$ uniformly integrable?

Published on 26 Mar 2026 - 8:03

score 48 · Answer 6 · 2026-03-27 06:51:58

48

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 27 Mar 2026 - 6:51

score 148 · Answer 7 · 2026-03-27 06:52:00

148

Views

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

Published on 27 Mar 2026 - 6:52

score 72 · Answer 8 · 2026-03-27 06:56:57

72

Views

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

Published on 27 Mar 2026 - 6:56

score 145 · Answer 9 · 2026-03-28 14:05:35

145

Views

How to show Tanaka's formula is the Doob-Meyer decomposition?

Published on 28 Mar 2026 - 14:05

score 164 · Answer 10 · 2020-02-11 19:48:50

164

Views

Prove Submartingale Inequality and Implication that Involve Weak $L^1$ Inequality

Published on 11 Feb 2020 - 19:48

score 41 · Answer 11 · 2026-03-26 19:20:12

41

Views

Show that $\mathbb{E}[\sup_{0 \leq s \leq t} M^4_s] \leq \frac43 \mathbb{E}[M_t \sup_{0 \leq s \leq t} M^3_s] $

Published on 26 Mar 2026 - 19:20

score 23 · Answer 12 · 2020-02-12 17:53:50

23

Views

why can $\mathbb{E}_{x}[M^{\lambda}_{\inf{\{m, T_0, T_a\}}}]$ be decomposed this way?

Published on 12 Feb 2020 - 17:53

score 27 · Answer 13 · 2020-02-12 20:39:08

27

Views

Clarification on the definition of a martingale

Published on 12 Feb 2020 - 20:39

score 348 · Answer 14 · 2026-03-27 06:51:20

348

Views

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

Published on 27 Mar 2026 - 6:51

score 56 · Answer 15 · 2020-02-13 11:09:21

56

Views

$E[X_T 1_{T\ge t} | \mathscr{F}_{t \wedge T}] = E[X_T 1_{T\ge t} | \mathscr{F}_t]$ holds?

Published on 13 Feb 2020 - 11:09

List Question

Show that $(V_{n})_{n \le N}$ is a $\mathcal{F}_n$-martingale

Show that $(M_{n})$ with $M_{n}=(X_{n}-\mathbb{E}(X_{n}))^{2}-\operatorname{Var}(X_{n})$ is a $\mathcal{F}_{n}$-martingale

Finding a regular process which is a martingale

Doob's Decomposition Theorem and Uniform Integrability

If $\mathbb E[\sup_{t\in [0,T]}|X_t|]<\infty$, is $(X_t)_{t\in [0,T]}$ uniformly integrable?

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 to show Tanaka's formula is the Doob-Meyer decomposition?

Prove Submartingale Inequality and Implication that Involve Weak $L^1$ Inequality

Show that $\mathbb{E}[\sup_{0 \leq s \leq t} M^4_s] \leq \frac43 \mathbb{E}[M_t \sup_{0 \leq s \leq t} M^3_s] $

why can $\mathbb{E}_{x}[M^{\lambda}_{\inf{\{m, T_0, T_a\}}}]$ be decomposed this way?

Clarification on the definition of a martingale

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

$E[X_T 1_{T\ge t} | \mathscr{F}_{t \wedge T}] = E[X_T 1_{T\ge t} | \mathscr{F}_t]$ holds?

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