List questions from brownian-motion

Published on 22 Jan 2019 - 0:01

213

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Is a continuous function of (integrable) Brownian motion always integrable?

Published on 25 Mar 2026 - 16:08

497

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Are $\int_0^t \text{sign}(W_u) \, dW_u$ and $W_t$ independent for a Brownian motion $(W_t)_{t \geq 0}$?

Published on 22 Jan 2019 - 11:01

163

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Ito Isometry for Brownian Bridge

Published on 22 Jan 2019 - 21:33

440

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Brownian motion maximum inequality

Published on 22 Jan 2019 - 21:43

74

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Applying Ito's formula to $D^x(t)=(\partial/\partial x)S(t)$

Published on 26 Mar 2026 - 4:50

557

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Conditional expectation of Brownian motion given stopping-time sigma algebra

Published on 25 Mar 2026 - 16:02

27

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Where is the flaw in my reasoning when computing the expectation of a Brownian motion dependent on a rate one Poisson process?

Published on 24 Jan 2019 - 14:01

43

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$\mathbb{P}\left \{\sup_{t\in [0,\delta]} B_{t} \geq \delta^{2/3}\right\} \geq 1-\delta^\alpha$ as $\delta$ tends to zero.

Published on 24 Jan 2019 - 18:19

753

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How to prove that the exit time of a Brownian motion is a stopping time?

Published on 25 Mar 2026 - 16:02

237

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If $W_t$ is a Wiener process, what is $ \operatorname{Var}(W_t+W_s)$?

Published on 26 Jan 2019 - 19:58

64

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Understanding specific step in Wald Lemma's proof

Published on 27 Jan 2019 - 12:15

714

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Cosine of a Wiener process

Published on 25 Mar 2026 - 23:36

65

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Convergence of stochastic integral to Brownian motion

Published on 26 Mar 2026 - 3:11

29

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Existence of a unique solution of $dX_t=X_tB_tdB_t+X_tB_tdt, X_0=1$

Published on 28 Jan 2019 - 18:27

List Question

Doobs Martingale inequality

Is a continuous function of (integrable) Brownian motion always integrable?

Are $\int_0^t \text{sign}(W_u) \, dW_u$ and $W_t$ independent for a Brownian motion $(W_t)_{t \geq 0}$?

Ito Isometry for Brownian Bridge

Brownian motion maximum inequality

Applying Ito's formula to $D^x(t)=(\partial/\partial x)S(t)$

Conditional expectation of Brownian motion given stopping-time sigma algebra

Where is the flaw in my reasoning when computing the expectation of a Brownian motion dependent on a rate one Poisson process?

$\mathbb{P}\left \{\sup_{t\in [0,\delta]} B_{t} \geq \delta^{2/3}\right\} \geq 1-\delta^\alpha$ as $\delta$ tends to zero.

How to prove that the exit time of a Brownian motion is a stopping time?

If $W_t$ is a Wiener process, what is $ \operatorname{Var}(W_t+W_s)$?

Understanding specific step in Wald Lemma's proof

Cosine of a Wiener process

Convergence of stochastic integral to Brownian motion

Existence of a unique solution of $dX_t=X_tB_tdB_t+X_tB_tdt, X_0=1$

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