List questions from brownian-motion

Published on 15 Jul 2015 - 15:50

195

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Given a geometric Brownian motion, obtain a recurrence relation for moment $\mathbb{E}X_k^q$ and deduce $\mathbb{E}_k^q=\alpha^k(ah^{1/2},q)$

Published on 29 Mar 2026 - 5:34

39

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what would be power series of $x_t = e^{\beta_t} $ if $\beta_t$ is a Brownian motion process?

Published on 17 Jul 2015 - 14:04

284

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Showing a process satisfies an SDE

Published on 29 Mar 2026 - 5:34

410

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Brownian motion needs to be defined continuous for every $\omega$ to be jointly measurable.

Published on 21 Jul 2015 - 4:46

172

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When is an Ornstein-Uhlenbeck process equivalent to Brownian motion up to a given time lag

Published on 21 Jul 2015 - 5:43

1.3k

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Translation invariance of Brownian motion

Published on 23 Jul 2015 - 16:48

308

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Compute the expected value of a brownian motion

Published on 24 Jul 2015 - 3:38

200

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The entrance law of a Brownian motion with absorbing boundary

Published on 24 Jul 2015 - 17:20

584

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Understanding the Markov property of Brownian motion

Published on 02 Apr 2026 - 3:42

208

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How to prove that this process is always positive?

Published on 29 Mar 2026 - 5:35

209

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Reflection principle in the proof of the distribution of $M_t - W_t$ (Brownian motion)

Published on 26 Jul 2015 - 16:31

2.3k

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Intuition about Blumenthal's 0-1 law

Published on 26 Jul 2015 - 16:33

451

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Tail field versus germ field of Brownian motion

Published on 27 Jul 2015 - 18:54

92

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Distribution of hitting time for two border brownian motion

Published on 28 Jul 2015 - 19:08

List Question

Distribution of stochastic integral w.r. to brownian motion

Given a geometric Brownian motion, obtain a recurrence relation for moment $\mathbb{E}X_k^q$ and deduce $\mathbb{E}_k^q=\alpha^k(ah^{1/2},q)$

what would be power series of $x_t = e^{\beta_t} $ if $\beta_t$ is a Brownian motion process?

Showing a process satisfies an SDE

Brownian motion needs to be defined continuous for every $\omega$ to be jointly measurable.

When is an Ornstein-Uhlenbeck process equivalent to Brownian motion up to a given time lag

Translation invariance of Brownian motion

Compute the expected value of a brownian motion

The entrance law of a Brownian motion with absorbing boundary

Understanding the Markov property of Brownian motion

How to prove that this process is always positive?

Reflection principle in the proof of the distribution of $M_t - W_t$ (Brownian motion)

Intuition about Blumenthal's 0-1 law

Tail field versus germ field of Brownian motion

Distribution of hitting time for two border brownian motion

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