# Proving that a process is a brownian motion: How do I show independent increments?

$$W_t$$ is a brownian motion and I want to show that $$W^*_t=(-W_t)$$ is also a brownian motion. I can easily show the distribution the new variable: $$W^*_t \sim N(0,t)$$.

But one of the properties of brownian motion is that the process has independent increments; how do I argue for that?

• Maybe it helps to show that if $X$ and $Y$ are independent, then $-X$ and $-Y$ are independent as well. – Shashi Dec 8 '18 at 14:30