Question

Details in non-Hölder continuity of Brownian Motion

score 195 · Answer 1 · 2026-04-12 21:54:40

195

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Details in non-Hölder continuity of Brownian Motion

Published on 12 Apr 2026 - 21:54

score 229 · Answer 2 · 2026-05-10 17:13:34

229

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Martingale related to exponential martingale

Published on 10 May 2026 - 17:13

score 315 · Answer 3 · 2026-04-10 16:59:35

315

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Derivative of a random process using a Karhunen-Loève-expansion/basis expansion

Published on 10 Apr 2026 - 16:59

score 369 · Answer 4 · 2026-05-10 14:49:17

369

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If $W_t$ is a Wiener process, why is the limit $\lim_{n \rightarrow \infty} \sum_{i=0}^{n-1} (W_{S_{i+1}} - W_{s_i})^2$ equal to $t$?

Published on 10 May 2026 - 14:49

score 352 · Answer 5 · 2026-05-07 19:19:04

352

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Why the Brownian motion stopped at the local time is a martingale?

Published on 07 May 2026 - 19:19

score 395 · Answer 6 · 2026-05-10 15:45:44

395

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How can I compute the expectation of a squared Ito Integral?

Published on 10 May 2026 - 15:45

score 56 · Answer 7 · 2026-04-13 19:27:12

56

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Compute $\mathbb{E}[W(t)\int_0^t W(s)ds]$

Published on 13 Apr 2026 - 19:27

score 73 · Answer 8 · 2026-05-10 16:57:35

73

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find 2 local martingales M(t) and N(t) such that M(T)=N(T),but for t<T,M(t) $\ne$ N(t)

Published on 10 May 2026 - 16:57

score 508 · Answer 9 · 2026-05-10 16:05:12

508

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Calculation Resolvent/$\alpha$-Potential of Brownian Motion/Wiener Process

Published on 10 May 2026 - 16:05

score 162 · Answer 10 · 2026-04-16 08:44:39

Is the Brownian motion $B_{t_i}$ independent from the increments $B_{t_k}-B_{t_{k-1}}$ (where $t_i <t_{k-1}<t_k$)

score 326 · Answer 11 · 2026-04-25 03:30:29

326

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Proof of Non-differentiability of Brownian motion using local times

Published on 25 Apr 2026 - 3:30

score 64 · Answer 12 · 2026-04-19 16:55:00

64

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Proving that the square of a particular Brownian Motion approaches zero as its Quadratic Variation approaches 0?

Published on 19 Apr 2026 - 16:55

score 76 · Answer 13 · 2026-05-11 02:50:24

76

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$M(t)=W(t)^{4} -$ $6\int_0^t W(s)^{2} \,ds$ is a martingale where $W(t)$ represents the standard Brownian Motion

Published on 11 May 2026 - 2:50

score 160 · Answer 14 · 2026-05-10 13:51:01

160

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Show that $P^0( a<W_\theta \leq b \vert W_t=y)\leq P^0( a<W_\theta \leq b \vert W_t=\frac{a+b}{2})$

Published on 10 May 2026 - 13:51

score 280 · Answer 15 · 2026-04-14 15:23:19

280

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Intuition on Expectation of Brownian motion starting at $x \in \mathbb{R}$ at a time $\epsilon>0$

Published on 14 Apr 2026 - 15:23

List Question

Details in non-Hölder continuity of Brownian Motion

Martingale related to exponential martingale

Derivative of a random process using a Karhunen-Loève-expansion/basis expansion

If $W_t$ is a Wiener process, why is the limit $\lim_{n \rightarrow \infty} \sum_{i=0}^{n-1} (W_{S_{i+1}} - W_{s_i})^2$ equal to $t$?

Why the Brownian motion stopped at the local time is a martingale?

How can I compute the expectation of a squared Ito Integral?

Compute $\mathbb{E}[W(t)\int_0^t W(s)ds]$

find 2 local martingales M(t) and N(t) such that M(T)=N(T),but for t<T,M(t) $\ne$ N(t)

Calculation Resolvent/$\alpha$-Potential of Brownian Motion/Wiener Process

Is the Brownian motion $B_{t_i}$ independent from the increments $B_{t_k}-B_{t_{k-1}}$ (where $t_i <t_{k-1}<t_k$)

Proof of Non-differentiability of Brownian motion using local times

Proving that the square of a particular Brownian Motion approaches zero as its Quadratic Variation approaches 0?

$M(t)=W(t)^{4} -$ $6\int_0^t W(s)^{2} \,ds$ is a martingale where $W(t)$ represents the standard Brownian Motion

Show that $P^0( a<W_\theta \leq b \vert W_t=y)\leq P^0( a<W_\theta \leq b \vert W_t=\frac{a+b}{2})$

Intuition on Expectation of Brownian motion starting at $x \in \mathbb{R}$ at a time $\epsilon>0$

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