On Martingale Inequalities in Non-commutative Stochastic Analysis

We develop a non-commutativeLpstochastic calculus for the Clifford stochastic integral, anL2theory of which has been developed by Barnett, Streater, and Wilde. The main results are certain non-commutativeLpinequalities relating Clifford integrals and their integrands. These results are applied to ex...

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Bibliographic Details
Published in:Journal of functional analysis 1998-10, Vol.158 (2), p.475-508
Main Authors: Carlen, Eric A, Krée, Paul
Format: Article
Language:English
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Summary:We develop a non-commutativeLpstochastic calculus for the Clifford stochastic integral, anL2theory of which has been developed by Barnett, Streater, and Wilde. The main results are certain non-commutativeLpinequalities relating Clifford integrals and their integrands. These results are applied to extend the domain of the Clifford integral fromL2toL1integrands, and we give applications to optional stopping of Clifford martingales, proving an analog of a Theorem of Burkholder: The stopped Clifford processFThas zero expectation providedET
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.1998.3299