Suppose that is a d-dimensional Brownian motion. Show that if then is a martingale. Let Wt be a Brownian motion, Show a.s. Show Suppose W is a Brownian motion and show that the Laplace...

Suppose that

is a d-dimensional Brownian motion. Show that if

then

is a martingale.

Let W_t
be a Brownian motion,

Show

a.s. Show

Suppose W is a Brownian motion and

show that the Laplace transform of the density of S is given by