# Quick Brownian Proof

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• November 23rd 2010, 03:44 PM
sirellwood
Quick Brownian Proof
Can anyone show that if Wt is a standard Brownian motion. Show that the process Yt = −Wt is also a standard Brownian motion?
• November 27th 2010, 01:26 PM
Focus
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 $Y_{t+s}-Y_s=W_s-W_{t+s}=-(W_{t+s}-W_s)$ and the rest follows from the stationary independent increments of BM.