# Brownian motion

1. Dec 13, 2008

### dirk_mec1

1. The problem statement, all variables and given/known data
Show that $$\frac{X ( a^2t) }{a}$$ is a brownian motion.

2. Relevant equations
http://img168.imageshack.us/img168/8453/83818601fz4.png [Broken]

3. The attempt at a solution
I found this in my lecture notes but isn't the proof just replacing (t-s) by a^2(t-s) and s by a^2 s and dividing through a?

http://img504.imageshack.us/img504/7958/95843783bk9.png [Broken]

Last edited by a moderator: May 3, 2017
2. Dec 13, 2008

### rochfor1

Is X(t) a brownian motion?

3. Dec 14, 2008

### dirk_mec1

Yes, I forgot to mention that!