Question

Let X be a semimartingale, prove that $[X,[X,X]^c] = 0$

score 54 · Answer 1 · 2023-02-22 20:28:33

54

Views

Let X be a semimartingale, prove that $[X,[X,X]^c] = 0$

Published on 22 Feb 2023 - 20:28

score 99 · Answer 2 · 2023-02-24 23:10:47

99

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Matrix Azuma Inequality with non-zero mean

Published on 24 Feb 2023 - 23:10

score 40 · Answer 3 · 2023-02-25 07:44:27

40

Views

Can this integrability assumption be weakened in a way that the stochastic integration by parts still holds?

Published on 25 Feb 2023 - 7:44

score 194 · Answer 4 · 2023-03-01 12:47:23

194

Views

Example of a martingale with non-independent increments and fixed variance

Published on 01 Mar 2023 - 12:47

score 77 · Answer 5 · 2026-02-23 10:06:17

77

Views

Given a local martingale $M$ the running supremum $N_t=\sup_{0\leq s\leq t}|M_s|$ is locally integrable

Published on 23 Feb 2026 - 10:06

score 74 · Answer 6 · 2023-03-03 21:22:20

74

Views

Is M defined as below a martingale?

Published on 03 Mar 2023 - 21:22

score 141 · Answer 7 · 2026-02-23 08:56:35

141

Views

Application of Cesaro lemma

Published on 23 Feb 2026 - 8:56

score 66 · Answer 8 · 2026-03-31 03:45:31

66

Views

Waiting time pattern in Levin , Peres

Published on 31 Mar 2026 - 3:45

score 44 · Answer 9 · 2026-03-28 10:56:19

44

Views

Prove that $Z_{n} = X_{n} 1_{ (T>n)} + Y_{n} 1_{ (T \leq n)}$ is a supermartingale.

Published on 28 Mar 2026 - 10:56

score 75 · Answer 10 · 2023-03-11 20:36:30

75

Views

Independence of random variable to sigma-algebra generated by previous ones

Published on 11 Mar 2023 - 20:36

score 33 · Answer 11 · 2026-02-23 10:06:00

33

Views

If $B$ is a Brownian motion and $f \in \mathcal C^2(\mathbb R^n)$ harmonic, then $f(B)$ is a continuous martingale

Published on 23 Feb 2026 - 10:06

score 75 · Answer 12 · 2026-02-23 10:04:42

75

Views

Local martingale: how is $\sup_{s \in[0, t]}\left|M_s\right|$ measurable?

Published on 23 Feb 2026 - 10:04

score 93 · Answer 13 · 2026-02-23 10:06:18

93

Views

A proof of Lévy's theorem: how to obtain the independence $X_t-X_s \perp \mathcal{F}_s$?

Published on 23 Feb 2026 - 10:06

score 49 · Answer 14 · 2026-02-23 10:05:13

49

Views

Assume $M^{\tau_n}$ is uniformly integrable. Is $X^{\tau_n}$ uniformly integrable?

Published on 23 Feb 2026 - 10:05

score 87 · Answer 15 · 2026-03-28 11:03:51

87

Views

Brownian motion: how is $\mathbb E [\sup_{t \ge 0} |\langle M\rangle_{t \wedge \tau_n}|^2] < \infty$ satisfied?

Published on 28 Mar 2026 - 11:03

List Question

Let X be a semimartingale, prove that $[X,[X,X]^c] = 0$

Matrix Azuma Inequality with non-zero mean

Can this integrability assumption be weakened in a way that the stochastic integration by parts still holds?

Example of a martingale with non-independent increments and fixed variance

Given a local martingale $M$ the running supremum $N_t=\sup_{0\leq s\leq t}|M_s|$ is locally integrable

Is M defined as below a martingale?

Application of Cesaro lemma

Waiting time pattern in Levin , Peres

Prove that $Z_{n} = X_{n} 1_{ (T>n)} + Y_{n} 1_{ (T \leq n)}$ is a supermartingale.

Independence of random variable to sigma-algebra generated by previous ones

If $B$ is a Brownian motion and $f \in \mathcal C^2(\mathbb R^n)$ harmonic, then $f(B)$ is a continuous martingale

Local martingale: how is $\sup_{s \in[0, t]}\left|M_s\right|$ measurable?

A proof of Lévy's theorem: how to obtain the independence $X_t-X_s \perp \mathcal{F}_s$?

Assume $M^{\tau_n}$ is uniformly integrable. Is $X^{\tau_n}$ uniformly integrable?

Brownian motion: how is $\mathbb E [\sup_{t \ge 0} |\langle M\rangle_{t \wedge \tau_n}|^2] < \infty$ satisfied?

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