On the rough-paths approach to non-commutative stochastic calculus

Aurélien Deya (1) , Schott René (1)

1 Probabilités et statistiques

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.

Mots clés: non-commutative stochastic calculus; rough paths theory; free Brownian motion; approximation results

Domaines: Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Aurélien Deya, Schott René. On the rough-paths approach to non-commutative stochastic calculus. 2013. ⟨hal-00781383v1⟩