Abstract.
We define stochastic integrals with respect to free Brownian motion, and show that they satisfy Burkholder-Gundy type inequalities in operator norm. We prove also a version of Itô's predictable representation theorem, as well as product form and functional form of Itô's formula. Finally we develop stochastic analysis on the free Fock space, in analogy with stochastic analysis on the Wiener space.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 6 February 1998
Rights and permissions
About this article
Cite this article
Biane, P., Speicher, R. Stochastic calculus with respect to free Brownian motion and analysis on Wigner space. Probab Theory Relat Fields 112, 373–409 (1998). https://doi.org/10.1007/s004400050194
Issue Date:
DOI: https://doi.org/10.1007/s004400050194