Define the H1 norm of a martingale by Prove that this is a norm. Does there exist a uniformly integrable continuous martingale that is not in H1? Let W be a Brownian motion and let T be a stopping...

Define the H₁
norm of a martingale by

Prove that this is a norm. Does there exist a uniformly integrable continuous martingale that is not in H₁?

Let W be a Brownian motion and let T be a stopping time. Prove that if

then

EWT = 0.

Chapter 13