A non-commutative version of Lépingle–Yor martingale inequality

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

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Bibliographic Details
Published in	Statistics & probability letters Vol. 91; pp. 52 - 54
Main Author	Qiu, Yanqi
Format	Journal Article
Language	English
Published	Elsevier B.V 01.08.2014
Subjects	Lépingle–Yor inequality Non-commutative martingales Lépingle–Yor inequality Non-commutative martingales 46L53
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Summary:	Let (fn)n=1N be a stochastic process adapted to the filtration (ℱn)n=0N. An inequality of D. Lépingle and M. Yor states that E[(∑n=1N\|En−1(fn)\|2)1/2]≤2E[(∑n=1N\|fn\|2)1/2]. We generalize this inequality to non-commutative martingale setting.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2014.04.007