Hi!!!
I need some help at the following exercise...
Let B be a typical brownian motion with μ>0 and x ε R. X_{t}:=x+B_{t}+μt, for each t>=0, a brownian motion with velocity μ that starts at x. For r ε R, T_{r}:=inf{s>=0:X_{s}=r} and φ(r):=exp(-2μr). Show that M_{t}:=φ(X_{t}) for t>=0 is martingale.
Could you tell me the purpose of T_{r}??