Further Inequalities
There are further (sub)martingale inequalities also due to Doob. With the same assumptions on X as above, let
and for p ≥ 1 let
In this notation, Doob's inequality as stated above reads
The following inequalities also hold: for p = 1,
and, for p > 1,
Read more about this topic: Doob's Martingale Inequality
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