List questions from brownian-motion

Published on 14 Apr 2026 - 11:58

259

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First Passage Time for a Drifted Brownian Motion

Published on 10 Apr 2026 - 18:29

54

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$\mathbb{P}(\limsup_{n\rightarrow\infty}\frac{W(n)}{\sqrt{n}}>c)\geq \lim_{n\rightarrow{\infty}}\mathbb{P}(W(n)/\sqrt{n}>c)>0$

Published on 17 Apr 2026 - 15:49

67

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Limit using Itô isometry

Published on 13 Apr 2026 - 17:57

186

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Density function of a Brownian motion conditioning on a first exit time

Published on 09 Apr 2026 - 16:18

144

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Brownian motion, correlation coefficient, expectation function

Published on 13 Apr 2026 - 4:10

56

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Condition for martingale

Published on 13 Apr 2026 - 17:57

608

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Combining the derivative of two Brownian motions into one.

Published on 12 Apr 2026 - 9:03

81

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$\mathbb{E}[(\sup_{1\leq t\leq\infty}W(t)/t)^2]$ where $W(t)$ is a Wiener process

Published on 12 Apr 2026 - 7:20

70

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Verify whether $\mathbb{E}\int_{0}^{\infty}\frac{|B_t|}{(1+B_t^2)^2}\mathrm{d}t < \infty$

Published on 15 Apr 2026 - 18:11

455

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Quadratic variation and measure change

Published on 12 Apr 2026 - 15:25

140

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Ornstein-Uhlenbeck Bridge as a Random Walk Limit (The Urn Game)

Published on 09 Apr 2026 - 21:19

298

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Reflection principle, brownian motion

Published on 10 Apr 2026 - 23:07

150

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Need some clarification for the proof that a martingale is a Brownian motion with change of time.

Published on 13 Apr 2026 - 19:46

82

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Local time formula: $L_t=\lim_{h\to0}\frac{1}{h}\int_0^t \left(P_hf(B_s)-f(B_s)\right) \text{d}s\text{ a.s.}$

Published on 17 Apr 2026 - 3:31

List Question

Integrate an indicator against Brownian motion

First Passage Time for a Drifted Brownian Motion

$\mathbb{P}(\limsup_{n\rightarrow\infty}\frac{W(n)}{\sqrt{n}}>c)\geq \lim_{n\rightarrow{\infty}}\mathbb{P}(W(n)/\sqrt{n}>c)>0$

Limit using Itô isometry

Density function of a Brownian motion conditioning on a first exit time

Brownian motion, correlation coefficient, expectation function

Condition for martingale

Combining the derivative of two Brownian motions into one.

$\mathbb{E}[(\sup_{1\leq t\leq\infty}W(t)/t)^2]$ where $W(t)$ is a Wiener process

Verify whether $\mathbb{E}\int_{0}^{\infty}\frac{|B_t|}{(1+B_t^2)^2}\mathrm{d}t < \infty$

Quadratic variation and measure change

Ornstein-Uhlenbeck Bridge as a Random Walk Limit (The Urn Game)

Reflection principle, brownian motion

Need some clarification for the proof that a martingale is a Brownian motion with change of time.

Local time formula: $L_t=\lim_{h\to0}\frac{1}{h}\int_0^t \left(P_hf(B_s)-f(B_s)\right) \text{d}s\text{ a.s.}$

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