# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 36: Scale-Invariance of Brownian Motion

Brownian motion (also known as the Wiener process (after Norbert Wiener)) is scale-invariant, a feature which distinguishes it from other stochastic processes like standard random walks. This means that if $W_t$ is a Wiener process, then for any non-zero constant $\alpha$,

$\alpha ^{-1} W_{\alpha ^2 t}$

is also a Wiener process.