List questions from brownian-motion

Published on 01 Apr 2026 - 14:59

50

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Solve $dX_t=(a+bW_t)dt+cdW_t.$

Published on 26 Mar 2026 - 4:32

247

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Is this stopping time $\tau = \inf\{ t \ge 0: B(t) \in \{-a, b\}\}$ bounded?

Published on 26 Mar 2026 - 23:11

109

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$B_t$ has same law of $-B_t$

Published on 05 Jan 2020 - 11:33

56

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Brownian motion and stopping times - Check that two events are the same

Published on 26 Mar 2026 - 23:11

1.8k

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What is $P(B_1 > 0, B_2 > 0)$ , where $B_t$ is a Brownian Motion at time $t$?

Published on 01 Apr 2026 - 16:29

42

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What is the correlation between $2$ Brownian motions at time $t_1$ and $t_2?$ Assume that they are jointly normal with correlation $\rho.$

Published on 01 Apr 2026 - 16:26

59

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Is $\max_{s \in [0,1]} B_s = B_1$ where $B_s \sim \mathcal{N}(0,s)$

Published on 29 Mar 2026 - 19:11

312

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how to compute the cross variation process here?

Published on 26 Mar 2026 - 4:29

97

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show that $\mathbb{E}\left(B_{1}^{2 n}\right)=(2 n-1) \mathbb{E}\left(B_{1}^{2 n-2}\right) $ using Ito's calculus

Published on 27 Mar 2026 - 23:48

422

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Is Ito's lemma also valid with stopped integrals?

Published on 27 Mar 2026 - 2:50

376

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Ito's Isometry and integrands in $\lambda^2_{\text{loc}}$

Published on 27 Mar 2026 - 23:57

347

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Why is this Brownian motion event not measurable w.r.t. the natural filtration?

Published on 26 Mar 2026 - 3:01

158

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Ito process with a brownian motion with drift

Published on 28 Mar 2026 - 6:58

71

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Complex Brownian motion and expectation of stopped process

Published on 26 Mar 2026 - 23:09

List Question

Prove $X_t = {W_t}^3 - 3\int^{t}_{0} W_s \, ds$ is a martingale using definition

Solve $dX_t=(a+bW_t)dt+cdW_t.$

Is this stopping time $\tau = \inf\{ t \ge 0: B(t) \in \{-a, b\}\}$ bounded?

$B_t$ has same law of $-B_t$

Brownian motion and stopping times - Check that two events are the same

What is $P(B_1 > 0, B_2 > 0)$ , where $B_t$ is a Brownian Motion at time $t$?

What is the correlation between $2$ Brownian motions at time $t_1$ and $t_2?$ Assume that they are jointly normal with correlation $\rho.$

Is $\max_{s \in [0,1]} B_s = B_1$ where $B_s \sim \mathcal{N}(0,s)$

how to compute the cross variation process here?

show that $\mathbb{E}\left(B_{1}^{2 n}\right)=(2 n-1) \mathbb{E}\left(B_{1}^{2 n-2}\right) $ using Ito's calculus

Is Ito's lemma also valid with stopped integrals?

Ito's Isometry and integrands in $\lambda^2_{\text{loc}}$

Why is this Brownian motion event not measurable w.r.t. the natural filtration?

Ito process with a brownian motion with drift

Complex Brownian motion and expectation of stopped process

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