Okay, this one has been bugging (and p***ing) me...
We have iid rv's where and
So for , is a martingale (with the natural filtration)
Let be the stopped martingale, where (b is another positive integer)
Then I have to prove, using the convergence of , that .
And I don't know how to do it (I've been scrabbling on it, without finding a formal proof...).
Thanks for any hint...