Can anyone show that if Wt is a standard Brownian motion. Show that the process Yt = −Wt is also a standard Brownian motion?
Just check the definitions. Distribution and continuity is obvious, so the only issue is the stationarity and independence of the increments. Use a simple calculation $\displaystyle Y_{t+s}-Y_s=W_s-W_{t+s}=-(W_{t+s}-W_s)$ and the rest follows from the stationary independent increments of BM.