Let B(t) be a Brownian motion. Show that the following processes are Brownian motions: 1. X(t)...

 

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Let B(t) be a Brownian motion. Show that the following processes are Brownian motions: 1. X(t) = -B(t). 2. X(t) = B(T) – B(T-t), 0≤t≤T. 3. X(t)=cB(t/c²), where c is a constant. 4. X(t) = tB(1/t), t > 0, and X (0) = 0. Let B(t) be a Brownian motion. Show that the following processes are Brownian motions: 1. X(t) = -B(t). 2. X(t) = B(T) – B(T-t), 0≤t≤T. 3. X(t)=cB(t/c²), where c is a constant. 4. X(t) = tB(1/t), t > 0, and X (0) = 0.

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1 Xt Bt is a Brownian motion since it is a linear transformation of a Brownian motion This follows f... View the full answer