Suppose W is a Brownian motion on [0, 1]. Let Show that Yt is a Brownian motion on [0, 1]. This exercise shows that the projection of a d-dimensional Brownian motion onto a hyper plane yields a...

Suppose W is a Brownian motion on [0, 1]. Let

Show that Y_t
is a Brownian motion on [0, 1].

This exercise shows that the projection of a d-dimensional Brownian motion onto a hyper plane yields a one-dimensional Brownian motion. Suppose

is a d-dimensional Brownian motion started from 0 and

Show that


is a one-dimensional Brownian motion started from 0.