List questions from stopping-times

Published on 16 Feb 2023 - 14:52

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When Convergence Implies Integrable Stopping Times

Published on 21 Feb 2023 - 15:54

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How to deal with discontinuous path in brownian motion?

Published on 22 Feb 2023 - 2:55

78

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Show that $\inf\{t>0: X_t(\omega)\in G\}$ is an optional time.

Published on 26 Feb 2023 - 22:15

113

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Concerning Proposition 1.1.32 of Jacod and Shiryaev

Published on 27 Feb 2023 - 18:38

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Is $\{\tau+\sigma<k\}\in \mathcal{F}_k$?

Published on 01 Mar 2023 - 13:01

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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

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

Published on 11 Mar 2023 - 8:42

41

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Stopping time must be a.s. finite when defining RV

Published on 17 Mar 2023 - 17:15

49

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

Published on 23 Feb 2026 - 10:05

86

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

Published on 19 Mar 2023 - 12:50

132

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Brownian motion: how is DCT for conditional expectation applied on this stopped martingale?

Published on 19 Mar 2023 - 19:18

57

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Stopped martingale: is this a more direct proof to this question?

Published on 19 Mar 2023 - 22:46

96

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Show that $T$ is a stopping time

Published on 20 Mar 2023 - 13:32

65

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Let $M$ be a continuous martingale, $r >0$, and $\tau := \inf \{t \ge 0 : \langle M \rangle_t \ge r \}$. Then $M_\tau$ is square-integrable

Published on 20 Mar 2023 - 15:47

List Question

Proof of Début Theorem for right-continuous adapted process - III

When Convergence Implies Integrable Stopping Times

How to deal with discontinuous path in brownian motion?

Show that $\inf\{t>0: X_t(\omega)\in G\}$ is an optional time.

Concerning Proposition 1.1.32 of Jacod and Shiryaev

Is $\{\tau+\sigma<k\}\in \mathcal{F}_k$?

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

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

Stopping time must be a.s. finite when defining RV

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?

Brownian motion: how is DCT for conditional expectation applied on this stopped martingale?

Stopped martingale: is this a more direct proof to this question?

Show that $T$ is a stopping time

Let $M$ be a continuous martingale, $r >0$, and $\tau := \inf \{t \ge 0 : \langle M \rangle_t \ge r \}$. Then $M_\tau$ is square-integrable

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