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1 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine

Abstract : We study different possibilities to apply the principles of rough paths theory in a non-commutative probability setting. First, we extend previous results obtained by Capitaine, Donati-Martin and Victoir in Lyons- original formulation of rough paths theory. Then we settle the bases of an alternative non-commutative integration procedure, in the spirit of Gubinelli-s controlled paths theory, and which allows us to revisit the constructions of Biane and Speicher in the free Brownian case. New approximation results are also derived from the strategy.

Keywords : approximation results rough paths theory free Brownian motion non-commutative stochastic calculus

Author: Aurélien Deya - René Schott -

Source: https://hal.archives-ouvertes.fr/


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