Martingale

[mathmari]

Hi!!!

I need some help at the following exercise...

Let [MATH]B[/MATH] be a typical brownian motion with μ>0 and [MATH]x[/MATH] ε [MATH]R[/MATH]. [MATH] X_{t}:=x+B_{t}[/MATH]+μt, for each [MATH]t>=0[/MATH], a brownian motion with velocity μ that starts at [MATH]x[/MATH]. For [MATH]r[/MATH] ε [MATH]R[/MATH], [MATH]T_{r}[/MATH]:=inf{[MATH]s>=0:X_{s}=r[/MATH]} and φ([MATH]r[/MATH]):=exp(-2μr). Show that [MATH]M_{t}:=[/MATH]φ[MATH](X_{t})[/MATH] for t>=0 is martingale.

Edited May 7, 2013 by mathmari