Question: 1.*11. Let {Xn, 9?;;; n E N} be a [super]martingale satisfying the following condition. there exists a constant lv! such that for every n :::

1.*11. Let {Xn, 9?;;; n E N} be a [super]martingale satisfying the following condition. there exists a constant lv! such that for every n ::: 1:

0"{lXn - Xn-l ll:16n-l } ::: Ma.e.

where Xo = 0 and .% is trivial. Then for any two optional r.v.'s a and fJ such that ex ::: fJ and cSU(fJ)

£:-1 IXn XIl II·

We have

(YB) = Y B) = / 182 (Bn) Xn-Xn-d M(B).]

(YB) = Y B) = / 182 (Bn) Xn-Xn-d M(B).]

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