Let $\displaystyle {B}(t)$ be a Brownian motion. Show that the following processes are Brownian motions on [0,T].

1. $\displaystyle {X}(t)=-{B}(t)$.

2. $\displaystyle {X}(t)={B}(T-t) - {B}(T),$ where $\displaystyle {T}<+\infty$.

3. $\displaystyle {X}(t)=c{B}(t/{c}^2),$ where $\displaystyle {T}\leq+\infty$.

4. $\displaystyle {X}(t)=t{B}(1/t),t>0, $ and $\displaystyle {X}(0)=0$.

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