On the rough-paths approach to non-commutative stochastic calculus
Probability
2016-03-09 v2 Operator Algebras
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
Cite
@article{arxiv.1301.6238,
title = {On the rough-paths approach to non-commutative stochastic calculus},
author = {Aurélien Deya and René Schott},
journal= {arXiv preprint arXiv:1301.6238},
year = {2016}
}
Comments
in Journal of Functional Analysis, Elsevier, 2013