List questions from brownian-motion

Published on 17 Jun 2015 - 0:07

181

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Electrostatic capacity of two spheres with changing radii

Published on 29 Mar 2026 - 1:35

1k

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Expected Value and Variance of a GBM Function

Published on 08 Apr 2026 - 19:04

376

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$\sigma+$-field of a Brownian motion

Published on 18 Jun 2015 - 6:56

2k

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Show that $(W_t)_{t \geq 0}$ and $(W_t^2-t)_{t \geq 0}$ are not uniformly integrable

Published on 26 Mar 2026 - 12:50

47

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The length of the set which will be covered by Brownian motion in a time $t$

Published on 20 Jun 2015 - 16:32

401

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The quadratic variation of $B \cdot B$, where $B$ is a Brownian motion

Published on 23 Feb 2026 - 12:07

37

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Mean and variance regime-switching model

Published on 01 Apr 2026 - 6:04

93

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$ P(W_t - W_\tau > 0 \text{ and } \tau <t) = \frac{1}{2}P(\tau < t) $ for a stopping time $\tau$

Published on 23 Jun 2015 - 13:47

3.6k

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Variance of an integral of Brownian Motion

Published on 23 Jun 2015 - 16:41

180

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Calculating $ \mathbb E \left[e^{-\mu W_T } 1_\left( {\min W_t \leq a} \right) \right]$ for a Wiener process

Published on 04 Apr 2026 - 9:49

799

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Moment generating function of $(W_T, \max W_t)$

Published on 29 Mar 2026 - 7:33

1.1k

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joint distribution of $(W(1),W(3),W(3)-W(2))$ for a brownian motion $(W(t))_{t \geq 0}$

Published on 25 Jun 2015 - 19:36

819

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Conditional expectation $\mathbb E\left(\exp\left(\int_0^tX_sdB_s\right) \mid \mathcal F_t^X\right)$

Published on 07 Apr 2026 - 22:56

754

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Donsker's theorem and multidimensional CLT

Published on 23 Feb 2026 - 9:59

List Question

Basic question about the stochastic integral $\int \limits_{0}^{t} X(s) \,dM(s)$

Electrostatic capacity of two spheres with changing radii

Expected Value and Variance of a GBM Function

$\sigma+$-field of a Brownian motion

Show that $(W_t)_{t \geq 0}$ and $(W_t^2-t)_{t \geq 0}$ are not uniformly integrable

The length of the set which will be covered by Brownian motion in a time $t$

The quadratic variation of $B \cdot B$, where $B$ is a Brownian motion

Mean and variance regime-switching model

$ P(W_t - W_\tau > 0 \text{ and } \tau <t) = \frac{1}{2}P(\tau < t) $ for a stopping time $\tau$

Variance of an integral of Brownian Motion

Calculating $ \mathbb E \left[e^{-\mu W_T } 1_\left( {\min W_t \leq a} \right) \right]$ for a Wiener process

Moment generating function of $(W_T, \max W_t)$

joint distribution of $(W(1),W(3),W(3)-W(2))$ for a brownian motion $(W(t))_{t \geq 0}$

Conditional expectation $\mathbb E\left(\exp\left(\int_0^tX_sdB_s\right) \mid \mathcal F_t^X\right)$

Donsker's theorem and multidimensional CLT

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