Question

Why is $X_t=\sum\limits_{i=1}^n \int _0 ^t \frac{B_s^i}{\sqrt{(B_s^1)^2+\cdots + (B_s^n)^2}}dB_s^i$ a Brownian motion?

score 38 · Answer 1 · 2026-04-16 05:04:16

38

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Why is $X_t=\sum\limits_{i=1}^n \int _0 ^t \frac{B_s^i}{\sqrt{(B_s^1)^2+\cdots + (B_s^n)^2}}dB_s^i$ a Brownian motion?

Published on 16 Apr 2026 - 5:04

score 2.3k · Answer 2 · 2026-04-14 15:29:10

2.3k

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Is the definite time integral of a Brownian Motion a Markov process and a martingale?

Published on 14 Apr 2026 - 15:29

score 3.3k · Answer 3 · 2026-04-11 15:30:32

3.3k

Views

Expectation of Exit Time of Brownian Motion from Interval

Published on 11 Apr 2026 - 15:30

score 45 · Answer 4 · 2026-04-14 07:53:38

45

Views

(Brownian Motion) Incremental joint probability conditioned on past value

Published on 14 Apr 2026 - 7:53

score 112 · Answer 5 · 2026-04-13 22:13:07

112

Views

Problem from Ito and McKean book.

Published on 13 Apr 2026 - 22:13

score 1k · Answer 6 · 2026-04-15 17:08:09

1k

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The stopping time when $|B_t|=1$, $B_t$ is one dimensional standard Brownian motion

Published on 15 Apr 2026 - 17:08

score 4.3k · Answer 7 · 2026-04-14 20:54:48

4.3k

Views

Expectation and Variance of $e^{B_T}$ for Brownian motion $(B_t)_{t \geq 0}$

Published on 14 Apr 2026 - 20:54

score 47 · Answer 8 · 2026-04-15 15:27:13

47

Views

Looking for a version of Donsker's theorem where the $X_i$ aren't quite right.

Published on 15 Apr 2026 - 15:27

score 86 · Answer 9 · 2026-04-12 10:51:38

86

Views

For Brownian Motion definition, is pairwise independence of intervals sufficient?

Published on 12 Apr 2026 - 10:51

score 311 · Answer 10 · 2026-04-09 02:58:56

311

Views

Conditional Probability of two Standard Brownian Motions

Published on 09 Apr 2026 - 2:58

score 43 · Answer 11 · 2026-04-11 00:31:46

43

Views

Brwonian Process ITO Integral

Published on 11 Apr 2026 - 0:31

score 203 · Answer 12 · 2026-04-15 13:20:45

203

Views

Show that $\mathbb{P}(\sup_{s\leq t} |B_s|\geq x)\leq 2\mathbb{P}(|B_t|\geq x)$

Published on 15 Apr 2026 - 13:20

score 130 · Answer 13 · 2026-04-12 00:53:48

130

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Is the fractional part of Brownian motion equidistributed almost surely?

Published on 12 Apr 2026 - 0:53

score 270 · Answer 14 · 2026-04-08 14:51:26

270

Views

Geometric Brownian Motion Process Problem

Published on 08 Apr 2026 - 14:51

score 134 · Answer 15 · 2026-04-15 07:17:57

134

Views

What is the variance of the Fourier coefficients of Brownian motion?

Published on 15 Apr 2026 - 7:17

List Question

Why is $X_t=\sum\limits_{i=1}^n \int _0 ^t \frac{B_s^i}{\sqrt{(B_s^1)^2+\cdots + (B_s^n)^2}}dB_s^i$ a Brownian motion?

Is the definite time integral of a Brownian Motion a Markov process and a martingale?

Expectation of Exit Time of Brownian Motion from Interval

(Brownian Motion) Incremental joint probability conditioned on past value

Problem from Ito and McKean book.

The stopping time when $|B_t|=1$, $B_t$ is one dimensional standard Brownian motion

Expectation and Variance of $e^{B_T}$ for Brownian motion $(B_t)_{t \geq 0}$

Looking for a version of Donsker's theorem where the $X_i$ aren't quite right.

For Brownian Motion definition, is pairwise independence of intervals sufficient?

Conditional Probability of two Standard Brownian Motions

Brwonian Process ITO Integral

Show that $\mathbb{P}(\sup_{s\leq t} |B_s|\geq x)\leq 2\mathbb{P}(|B_t|\geq x)$

Is the fractional part of Brownian motion equidistributed almost surely?

Geometric Brownian Motion Process Problem

What is the variance of the Fourier coefficients of Brownian motion?

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