List questions from brownian-motion

89

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If $(B_t)$ is a Brownian motion, then $P(\sup_{t\in [0,\infty )}B_t=0)=P(\sup_{t\in [0,\infty )}B_t<\infty )$.

Published on 16 Apr 2026 - 5:22

167

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Malliavin derivative of stopped Brownian motion

Published on 09 Apr 2026 - 18:04

215

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What is the expected present discounted value of a variable following a geometric Brownian motion?

Published on 14 Apr 2026 - 5:37

184

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Evaluate the price of asset in log Black and Scholes model

Published on 16 Apr 2026 - 11:40

108

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$\mathbb{E}B_\tau$ where $\tau$ is defined as follows

Published on 12 Apr 2026 - 22:52

756

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Convolution with a convex function

Published on 13 Apr 2026 - 7:35

395

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Boundedness in probability of Stochastic Process

Published on 13 Apr 2026 - 8:09

542

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Conditional Expectation of Brownian motion using projection

Published on 19 Apr 2026 - 3:14

10.1k

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The variance of Brownian motion

Published on 15 Apr 2026 - 9:37

403

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Is the logarithm of a martingale still a martingale?

Published on 12 Apr 2026 - 4:49

106

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Distribution of $\tau/x^2$ where $\tau$ is first hitting time

Published on 13 Apr 2026 - 21:08

75

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Time transform of Brownian motion

Published on 13 Apr 2026 - 9:36

345

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Proving integrability of the martingale $\cosh(\lambda B_t)\textrm{e}^{-\frac12\lambda^2t}$

Published on 16 Apr 2026 - 11:03

144

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Problem with proving Brownian Motion

Published on 12 Apr 2026 - 11:45

143

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Intuition for $\mathbb{E}[\tau]=\infty$ but $\mathbb{P}(\tau = \infty)=0$

Published on 14 Apr 2026 - 1:22

List Question

If $(B_t)$ is a Brownian motion, then $P(\sup_{t\in [0,\infty )}B_t=0)=P(\sup_{t\in [0,\infty )}B_t<\infty )$.

Malliavin derivative of stopped Brownian motion

What is the expected present discounted value of a variable following a geometric Brownian motion?

Evaluate the price of asset in log Black and Scholes model

$\mathbb{E}B_\tau$ where $\tau$ is defined as follows

Convolution with a convex function

Boundedness in probability of Stochastic Process

Conditional Expectation of Brownian motion using projection

The variance of Brownian motion

Is the logarithm of a martingale still a martingale?

Distribution of $\tau/x^2$ where $\tau$ is first hitting time

Time transform of Brownian motion

Proving integrability of the martingale $\cosh(\lambda B_t)\textrm{e}^{-\frac12\lambda^2t}$

Problem with proving Brownian Motion

Intuition for $\mathbb{E}[\tau]=\infty$ but $\mathbb{P}(\tau = \infty)=0$

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