Stochastic calculus with respect to free Brownian motion and analysis on Wigner space |
| |
| Authors: | Philippe Biane Roland Speicher |
| |
| Affiliation: | CNRS, DMI, Ecole Normale Supérieure, 45, rue d'Ulm, 75005 Paris, France. e-mail: biane@dmi.ens,fr, FR
Institut für Angewandte Mathematik, Universit?t Heidelberg, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany. e-mail: roland.Speicher@urz.uni-heidelberg.de, DE
|
| |
| 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 It?'s predictable representation theorem, as well as product form and functional form of It?'s formula. Finally we develop stochastic analysis on the free Fock space, in analogy with stochastic analysis on the Wiener space. Received: 6 February 1998 |
| |
| Keywords: | Mathematics Subject Classification (1991): 60H05 46L50 81S25 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
