Question

d-dimensional Brownian motion and martingales

score 3.2k · Answer 1 · 2026-04-15 10:24:58

3.2k

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d-dimensional Brownian motion and martingales

Published on 15 Apr 2026 - 10:24

score 178 · Answer 2 · 2026-04-15 18:17:15

178

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Given the SDE: $dX_t=dB_t+b(X_t) dt$ with $(x,b(x)) \leq 0, \forall x \in \mathbb{R}^n$, prove that $E[|X_t|^2] \leq nt+E[|X_0|^2]$

Published on 15 Apr 2026 - 18:17

score 646 · Answer 3 · 2026-04-11 22:54:20

646

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Computing the limit of the expectation of a function of a stochastic process (phew!)

Published on 11 Apr 2026 - 22:54

score 504 · Answer 4 · 2026-04-15 20:13:00

504

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Absolute continuity of the distribution of $X_t=aB_t+bt$, $Y_t=a(t)B_t$ with respect to the Wiener measure

Published on 15 Apr 2026 - 20:13

score 226 · Answer 5 · 2026-04-14 21:15:02

226

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Mean and variance of this random variable

Published on 14 Apr 2026 - 21:15

score 2.9k · Answer 6 · 2026-04-10 10:32:06

2.9k

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Is the following a Wiener process?

Published on 10 Apr 2026 - 10:32

score 126 · Answer 7 · 2026-04-14 22:29:56

126

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Show that $\sup\limits_tX_t-t^{p/2}$ and $\sup\limits_t\left(\frac{X_t}{1+t^{p/2}}\right)^q$ have the same law

Published on 14 Apr 2026 - 22:29

score 139 · Answer 8 · 2026-04-14 10:01:28

139

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Simulating of GBM

Published on 14 Apr 2026 - 10:01

score 3.5k · Answer 9 · 2026-04-14 00:49:29

3.5k

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linear combination of two Wiener processes

Published on 14 Apr 2026 - 0:49

score 979 · Answer 10 · 2026-04-12 17:46:49

979

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Brownian Bridge Representation

Published on 12 Apr 2026 - 17:46

score 395 · Answer 11 · 2026-04-16 16:01:39

395

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The probability of a Brownian particle traveling a distance $L$ before returning to its point-of-origin

Published on 16 Apr 2026 - 16:01

score 924 · Answer 12 · 2026-04-11 21:05:34

924

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Convergence to Brownian motion integral

Published on 11 Apr 2026 - 21:05

score 114 · Answer 13 · 2026-04-09 15:11:49

114

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Convergence in $L^{2}(\Omega)$

Published on 09 Apr 2026 - 15:11

score 55 · Answer 14 · 2026-04-15 19:29:11

55

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Motion of the centroid of $k$ Brownian particles?

Published on 15 Apr 2026 - 19:29

score 470 · Answer 15 · 2026-04-17 15:00:37

470

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Variance for the distance between two Brownian particles vs. a Brownian particle and a stationary particle

Published on 17 Apr 2026 - 15:00

List Question

d-dimensional Brownian motion and martingales

Given the SDE: $dX_t=dB_t+b(X_t) dt$ with $(x,b(x)) \leq 0, \forall x \in \mathbb{R}^n$, prove that $E[|X_t|^2] \leq nt+E[|X_0|^2]$

Computing the limit of the expectation of a function of a stochastic process (phew!)

Absolute continuity of the distribution of $X_t=aB_t+bt$, $Y_t=a(t)B_t$ with respect to the Wiener measure

Mean and variance of this random variable

Is the following a Wiener process?

Show that $\sup\limits_tX_t-t^{p/2}$ and $\sup\limits_t\left(\frac{X_t}{1+t^{p/2}}\right)^q$ have the same law

Simulating of GBM

linear combination of two Wiener processes

Brownian Bridge Representation

The probability of a Brownian particle traveling a distance $L$ before returning to its point-of-origin

Convergence to Brownian motion integral

Convergence in $L^{2}(\Omega)$

Motion of the centroid of $k$ Brownian particles?

Variance for the distance between two Brownian particles vs. a Brownian particle and a stationary particle

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