List questions from brownian-motion

Published on 17 Mar 2026 - 7:19

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Why has $\sup_{s \in (0,t)} B_s$ the same distribution as $\sup_{s \in (0,t)} B_s-B_t$ for a Brownian motion $(B_t)_{t \geq 0}$?

Published on 24 Mar 2026 - 11:56

45

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Identity related to Brownian motion

Published on 24 Mar 2026 - 10:54

2.4k

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4th moment of a Wiener stochastic integral?

Published on 17 Mar 2026 - 3:09

319

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Optional Stopping Theorem for martingales

Published on 17 Mar 2026 - 12:02

663

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Discontinuous Brownian Motion

Published on 21 Mar 2026 - 22:35

3k

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Sample path of Brownian motion Hölder continuous?

Published on 17 Mar 2026 - 7:36

493

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Polar Brownian motion not recovering polar Laplacian?

Published on 17 Mar 2026 - 12:25

274

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Uniqueness of the parameters of an Ito process, given initial and terminal conditions

Published on 17 Mar 2026 - 7:07

224

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$dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$

Published on 17 Mar 2026 - 9:19

1.8k

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Why is $\int_0^t t \, dW_s$ not a martingale?

Published on 20 Mar 2026 - 8:59

2.3k

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Initial Distribution of Stochastic Differential Equations

Published on 17 Mar 2026 - 12:44

43

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Deriving law of motion for Brownian motion

Published on 24 Mar 2026 - 19:09

228

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Solving of enhanced Hull-White $dX_t = \frac{e^t-X_t}{t-2}dt + tdW_t$

Published on 17 Mar 2026 - 8:21

249

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Prove Brownian Bridge is Sampling Without Replacement

Published on 24 Mar 2026 - 19:00

List Question

Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$

Why has $\sup_{s \in (0,t)} B_s$ the same distribution as $\sup_{s \in (0,t)} B_s-B_t$ for a Brownian motion $(B_t)_{t \geq 0}$?

Identity related to Brownian motion

4th moment of a Wiener stochastic integral?

Optional Stopping Theorem for martingales

Discontinuous Brownian Motion

Sample path of Brownian motion Hölder continuous?

Polar Brownian motion not recovering polar Laplacian?

Uniqueness of the parameters of an Ito process, given initial and terminal conditions

$dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$

Why is $\int_0^t t \, dW_s$ not a martingale?

Initial Distribution of Stochastic Differential Equations

Deriving law of motion for Brownian motion

Solving of enhanced Hull-White $dX_t = \frac{e^t-X_t}{t-2}dt + tdW_t$

Prove Brownian Bridge is Sampling Without Replacement

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