Question

Details in non-Hölder continuity of Brownian Motion

score 192 · Answer 1 · 2018-04-17 07:15:12

192

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Details in non-Hölder continuity of Brownian Motion

Published on 17 Apr 2018 - 7:15

score 225 · Answer 2 · 2018-04-17 12:20:56

225

Views

Martingale related to exponential martingale

Published on 17 Apr 2018 - 12:20

score 312 · Answer 3 · 2018-04-17 15:21:01

312

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

Published on 17 Apr 2018 - 15:21

score 366 · Answer 4 · 2026-03-25 03:04:20

366

Views

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 25 Mar 2026 - 3:04

score 344 · Answer 5 · 2026-03-19 22:06:15

344

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

Published on 19 Mar 2026 - 22:06

score 392 · Answer 6 · 2026-03-25 03:01:37

392

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

Published on 25 Mar 2026 - 3:01

score 53 · Answer 7 · 2018-04-20 08:34:32

53

Views

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

Published on 20 Apr 2018 - 8:34

score 66 · Answer 8 · 2026-03-22 20:41:16

66

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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 22 Mar 2026 - 20:41

score 500 · Answer 9 · 2026-03-25 00:01:12

500

Views

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

Published on 25 Mar 2026 - 0:01

score 159 · Answer 10 · 2018-04-20 20:49:53

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 322 · Answer 11 · 2026-03-22 13:11:28

322

Views

Proof of Non-differentiability of Brownian motion using local times

Published on 22 Mar 2026 - 13:11

score 61 · Answer 12 · 2026-03-22 08:53:04

61

Views

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

Published on 22 Mar 2026 - 8:53

score 72 · Answer 13 · 2018-04-23 12:41:41

72

Views

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

Published on 23 Apr 2018 - 12:41

score 156 · Answer 14 · 2026-03-25 00:04:25

156

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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 25 Mar 2026 - 0:04

score 277 · Answer 15 · 2018-04-23 18:47:06

277

Views

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

Published on 23 Apr 2018 - 18:47

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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