Let Wt be a Brownian motion. Show that if α > 1/2, then using (3.9), and then use the Borel–Cantelli lemma. Let Wt be a one-dimensional Brownian motion and Prove that If W is a Brownian motion...

Let W_t
be a Brownian motion. Show that if α > 1/2, then

using (3.9), and then use the Borel–Cantelli lemma.

Let W_t
be a one-dimensional Brownian motion and

Prove that

If W is a Brownian motion and b is a constant, then the process X_t
= W_t
+ b_t
is a Brownian motion with drift. Prove that if b > 0, then

Chapter 4