List questions from stopping-times

Published on 26 Mar 2026 - 21:07

73

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Let $\tau : \Omega \to \{0,1,2...,\infty\}$ and $\{ X_n :n \geq 0\}$ be an adapted process. Is $\tau $ as topping time?

Published on 13 Dec 2020 - 20:11

715

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Optional stopping with a nonnegative supermartingale

Published on 14 Dec 2020 - 10:01

469

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Stopping time + constant

Published on 22 Dec 2020 - 21:47

31

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Two paths having the same stopping time

Published on 24 Dec 2020 - 12:27

188

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A square integrable a.s. convergent martingale with unbounded square variation process

Published on 27 Dec 2020 - 8:09

155

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Showing whether $\tau=\inf\{t:X_t=\sup_{0\leq t\leq T}X_t\}$ is a stopping time or not

Published on 02 Jan 2021 - 18:11

179

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Amoeba extinction probability

Published on 03 Jan 2021 - 15:03

122

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About a property of stopping times

Published on 06 Jan 2021 - 21:21

235

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Hitting time on a closed set of a continuous stochastic process is a stopping time.

Published on 12 Jan 2021 - 0:58

221

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Prove that the stopping time is finite

Published on 15 Jan 2021 - 10:45

55

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Compute $E(M_\sigma)$ and $E(e^{-\sigma})$

Published on 15 Jan 2021 - 19:14

33

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How to generalize the result $E(\sum_i^N X_i)=E(X_1)E(N)$ to the case where $X_i$ are not iid?

Published on 19 Jan 2021 - 9:45

87

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Set $M_t = 4B_t^2 + e^{4B_t -8t} -4t$. Find $\mathbb{E}(M_\sigma)$ for $\sigma = \inf(t \geq 0 : |B_t| = 1)$.

Published on 19 Jan 2021 - 17:18

127

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Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

Published on 20 Jan 2021 - 16:42

List Question

Problem about martingale, bounded stopping time

Let $\tau : \Omega \to \{0,1,2...,\infty\}$ and $\{ X_n :n \geq 0\}$ be an adapted process. Is $\tau $ as topping time?

Optional stopping with a nonnegative supermartingale

Stopping time + constant

Two paths having the same stopping time

A square integrable a.s. convergent martingale with unbounded square variation process

Showing whether $\tau=\inf\{t:X_t=\sup_{0\leq t\leq T}X_t\}$ is a stopping time or not

Amoeba extinction probability

About a property of stopping times

Hitting time on a closed set of a continuous stochastic process is a stopping time.

Prove that the stopping time is finite

Compute $E(M_\sigma)$ and $E(e^{-\sigma})$

How to generalize the result $E(\sum_i^N X_i)=E(X_1)E(N)$ to the case where $X_i$ are not iid?

Set $M_t = 4B_t^2 + e^{4B_t -8t} -4t$. Find $\mathbb{E}(M_\sigma)$ for $\sigma = \inf(t \geq 0 : |B_t| = 1)$.

Apply Ito's formula, prove a martingale, and calculate $\mathbb{E}(\tau)$

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