Noncommutative stochastic integration through decoupling

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:370

Article

Dirksen, Sjoerd

关键词: Noncommutative probability theory;    Stochastic integration;    Decoupling;    Noncommutative L(p)-spaces;    Khintchine inequalities;    Noncommutative Brownian motion;   

DOI  :  10.1016/j.jmaa.2010.04.062

来源: Elsevier

【 摘 要 】

We present an abstract approach to noncommutative stochastic integration in the context of a finite von Neumann algebra equipped with a normal, faithful, tracial state, with respect to processes with tensor or freely independent increments satisfying a stationarity condition, using a decoupling technique. We obtain necessary and sufficient conditions for stochastic integrability of L(p)-processes with respect to such integrators. We apply the theory to stochastic integration with respect to Boson and free Brownian motion. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free