Hi!!!
I need some help at the following exercise...
Let B be a typical brownian motion with μ>0 and x ε R. Xt:=x+Bt+
μt, for each t>=0, a brownian motion with velocity μ that starts at x. For r ε R, Tr:=inf{s>=0:Xs=r} and φ(r):=exp(-2μr). Show that Mt:=φ(Xt) for t>=0 is martingale.

Could you tell me the purpose of Tr??