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?