Dr. J and Fellow users,

I have a question on the "bounded" condition on a martingale.As we all know, for a stochastic process to be martingale, it needs to satisfy the "bounded" criterion i.e E(|X_t|)<inf for all t

Now, B_t where B is a BM is a martingale and B_t^3 is not.

Question is this: By direct integration, one can obtain

E(|B_t|)=(constant terms) * sqrt(t)

E(|B_t^3|)=(constant terms) * sqrt(t^3)

From the above results, it's not clear why E(|B_t|) is bounded as it should tend to inf (although at a slower rate) as t -->inf

What am I missing?

Regards,

SR