Suppose is a filtration satisfying the usual conditions, Pt is a Poisson process with respect to {Ft}, and Wt is a Brownian motion with respect to {Ft}. Show that if Wt + Pt has stationary and...

Suppose

is a filtration satisfying the usual conditions, P_t
is a Poisson process with respect to

{Ft}, and W_t
is a Brownian motion with respect to {Ft}. Show that if W_t
+ P_t
has stationary and independent increments, then P and W are independent processes.