Abstract
Let ( f n ) n = 1 N be a stochastic process adapted to the filtration ( ℱ n ) n = 0 N . An inequality of D. Lépingle and M. Yor states that E [ ( ∑ n = 1 N | E n − 1 ( f n ) | 2 ) 1 / 2 ] ≤ 2 E [ ( ∑ n = 1 N | f n | 2 ) 1 / 2 ] . We generalize this inequality to non-commutative martingale setting.
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