Question

$\mathbb{E}((M(\tau)-M(\rho))^2|F_{\rho})=\mathbb{E}(M^2(\tau)-M^2(\rho)|F_{\rho})$

score 39 · Answer 1 · 2026-03-27 13:25:35

39

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$\mathbb{E}((M(\tau)-M(\rho))^2|F_{\rho})=\mathbb{E}(M^2(\tau)-M^2(\rho)|F_{\rho})$

Published on 27 Mar 2026 - 13:25

score 157 · Answer 2 · 2026-03-28 14:44:32

157

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A doubt on the proof of Martingale Convergence Theorem on Jacod-Protter

Published on 28 Mar 2026 - 14:44

score 151 · Answer 3 · 2020-05-21 20:33:30

151

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Show this statement holds for a right continuous martingale.

Published on 21 May 2020 - 20:33

score 383 · Answer 4 · 2026-03-27 13:20:10

383

Views

Optional sampling theorem St. Petersburg paradox

Published on 27 Mar 2026 - 13:20

score 803 · Answer 5 · 2020-05-22 20:56:26

803

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$Var (X_n)= Var(X_0) +\sum_{k=0}^{n} Var (X_{k}-X_{k-1})$, Martingale Variance

Published on 22 May 2020 - 20:56

score 190 · Answer 6 · 2026-03-26 04:36:51

190

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A question about proof of Martingale Convergence Theorem. Why does the Uniform integrability imply the following fact?

Published on 26 Mar 2026 - 4:36

score 38 · Answer 7 · 2020-05-23 13:40:48

38

Views

How to prove $\mathbb{E}\{M_m 1_{\Psi}\}=\mathbb{E}\{M_n1_{\Psi}\}$, given that $n\geq m$, $\Psi\in\mathcal{F_m}$ and $(M_n)_{n\geq1}$ is martingale?

Published on 23 May 2020 - 13:40

score 79 · Answer 8 · 2020-05-23 15:28:12

79

Views

$\sigma$-algebra of the past intersection property

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score 49 · Answer 9 · 2026-02-23 06:20:57

49

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$X=M+A$ bounded semimartingale, then $M$ and $A$ are bounded? Counterexample?

Published on 23 Feb 2026 - 6:20

score 152 · Answer 10 · 2020-05-24 11:22:57

152

Views

Show martingality property for r.v. $S_{\infty}$, given some assumptions. Could you please detail your answer to my two points?

Published on 24 May 2020 - 11:22

score 53 · Answer 11 · 2020-05-24 13:42:55

53

Views

Given a martingale $Y=\mathbb{E}\{M_n|\mathcal{F}_n\}$, why does the below red inequality hold true?

Published on 24 May 2020 - 13:42

score 51 · Answer 12 · 2020-05-24 16:25:15

51

Views

Given a standard Brownian motion $W_t$, (i) what are the distributions of $|W_t|$ and $tW_t$? (ii) Are they martingales?

Published on 24 May 2020 - 16:25

score 563 · Answer 13 · 2026-03-25 19:06:59

563

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Some doubts in a part of the proof of Backwards Martingale Convergence Theorem (Jacod-Protter)

Published on 25 Mar 2026 - 19:06

score 197 · Answer 14 · 2026-03-27 11:48:54

197

Views

Given a sequence of i.i.d. random variables, prove a result involving conditional expectation by means of symmetry argument

Published on 27 Mar 2026 - 11:48

score 57 · Answer 15 · 2020-05-26 11:08:46

57

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Properties of Martingales

Published on 26 May 2020 - 11:08

List Question

$\mathbb{E}((M(\tau)-M(\rho))^2|F_{\rho})=\mathbb{E}(M^2(\tau)-M^2(\rho)|F_{\rho})$

A doubt on the proof of Martingale Convergence Theorem on Jacod-Protter

Show this statement holds for a right continuous martingale.

Optional sampling theorem St. Petersburg paradox

$Var (X_n)= Var(X_0) +\sum_{k=0}^{n} Var (X_{k}-X_{k-1})$, Martingale Variance

A question about proof of Martingale Convergence Theorem. Why does the Uniform integrability imply the following fact?

How to prove $\mathbb{E}\{M_m 1_{\Psi}\}=\mathbb{E}\{M_n1_{\Psi}\}$, given that $n\geq m$, $\Psi\in\mathcal{F_m}$ and $(M_n)_{n\geq1}$ is martingale?

$\sigma$-algebra of the past intersection property

$X=M+A$ bounded semimartingale, then $M$ and $A$ are bounded? Counterexample?

Show martingality property for r.v. $S_{\infty}$, given some assumptions. Could you please detail your answer to my two points?

Given a martingale $Y=\mathbb{E}\{M_n|\mathcal{F}_n\}$, why does the below red inequality hold true?

Given a standard Brownian motion $W_t$, (i) what are the distributions of $|W_t|$ and $tW_t$? (ii) Are they martingales?

Some doubts in a part of the proof of Backwards Martingale Convergence Theorem (Jacod-Protter)

Given a sequence of i.i.d. random variables, prove a result involving conditional expectation by means of symmetry argument

Properties of Martingales

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