Let be i.i.d. positive interger-value random variables with and . Define and recursively define
a) Show that is a martingale with respect to the filtration
b) Find and deduce that M_n has uniformly bounded variance if and only if
c) For , find
My proof so far.
a) This one is easy,
. So that proves that M_n is a martingale.
b) I'm having problem trying to break down this thing...
But how would I proceed from here? Thanks.