List questions from brownian-motion

Published on 27 Mar 2026 - 0:48

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Reference for quickest detection (sequential hypothesis testing) problems

Published on 26 Mar 2026 - 13:49

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$\bigcap_{t>T}\{|B_t| >0\}$ is not $\mathcal{F}_T$ measurable.

Published on 27 Mar 2026 - 14:58

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What do the "d" in SDE notation mean?

Published on 26 Mar 2026 - 13:49

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Why $\mathbb E[e^{i\xi(X_t-X_s)}1_F]=e^{-\frac{1}{2}(t-s)\xi^2}\mathbb P(F)$ for all $F\in \mathcal F_s$ implies that $X_t-X_s\perp F_s$?

Published on 05 May 2020 - 11:43

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Resnick Exercise 6.12 - Standard Brownian Motion

Published on 06 May 2020 - 1:06

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Resnick Exercise 6.21 - Find expectation and variance of Brownian Motion

Published on 06 May 2020 - 2:39

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Upper bound for density of standard Brownian Motion

Published on 30 Mar 2026 - 2:11

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Doob-Meyer Decomposition for $(W_{t}^{2}-t)^{2}$

Published on 28 Mar 2026 - 20:53

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Conditional expectation of an integrated GBM

Published on 28 Mar 2026 - 20:52

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Deriving stochastic integral $ X+\frac{1}{2}\int_t^T Z_s^2 ds - \int_t^TZ_s dB_s$

Published on 28 Mar 2026 - 21:06

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Proof check: Show that $B_{t} \sim N(0,t)$ is integrable

Published on 08 May 2020 - 8:42

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calculating expectation of standard Brownian motion $W_t$

Published on 30 Mar 2026 - 2:11

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Stochastic process, why this is that?

Published on 02 Apr 2026 - 18:20

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Negatively Correlated Diffusive Processes

Published on 08 May 2020 - 22:40

List Question

Multidimensional Ito Isometry

Reference for quickest detection (sequential hypothesis testing) problems

$\bigcap_{t>T}\{|B_t| >0\}$ is not $\mathcal{F}_T$ measurable.

What do the "d" in SDE notation mean?

Why $\mathbb E[e^{i\xi(X_t-X_s)}1_F]=e^{-\frac{1}{2}(t-s)\xi^2}\mathbb P(F)$ for all $F\in \mathcal F_s$ implies that $X_t-X_s\perp F_s$?

Resnick Exercise 6.12 - Standard Brownian Motion

Resnick Exercise 6.21 - Find expectation and variance of Brownian Motion

Upper bound for density of standard Brownian Motion

Doob-Meyer Decomposition for $(W_{t}^{2}-t)^{2}$

Conditional expectation of an integrated GBM

Deriving stochastic integral $ X+\frac{1}{2}\int_t^T Z_s^2 ds - \int_t^TZ_s dB_s$

Proof check: Show that $B_{t} \sim N(0,t)$ is integrable

calculating expectation of standard Brownian motion $W_t$

Stochastic process, why this is that?

Negatively Correlated Diffusive Processes

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