$W_t$ 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?

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

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