Let (Xt, Px ) be a Brownian motion. (1) Use the reflection principle to find This is the same as where T0 is the first time the Brownian motion hits 0. (2) Let Prove that and use this and...

Let (Xt, Px ) be a Brownian motion.

(1) Use the reflection principle to find

This is the same as

where T₀
is the first time the Brownian motion hits 0. (2) Let

Prove that

and use this and (1) to compute m(B(r)). By symmetry,

will be twice the value of m(B(r)).