Quantum white noise analysis and quantum stochastic equations
- Authors
- Belavkin, Viacheslav P.; Heo, Jaeseong; Ji, Un Cig
- Issue Date
- Jan-2011
- Publisher
- World Scientific Publishing Co
- Keywords
- Quantum Itô algebra; White Noise Analysis; Girsanov Transformation; Stochastic Master Equations
- Citation
- Infinite Dimensional Analysis, Quantum Probability and Related Topics, v.27, no. , pp.90 - 124
- Indexed
- SCIE
SCOPUS
- Journal Title
- Infinite Dimensional Analysis, Quantum Probability and Related Topics
- Volume
- 27
- Start Page
- 90
- End Page
- 124
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/169174
- DOI
- 10.1142/9789814338745_0005
- ISSN
- 0219-0257
- Abstract
- We review the basic concepts of quantum stochastic analysis using the universal Itô B*-algebra approach. The thermal quantum white noise as a noncommutative analog of the Lévy-Itô process is characterized in terms of the modular B*-Itô algebra. The main notions and results of classical and quantum stochastics are reformulated in this unifying approach. The Belavkin master equation for a quasi-Markov quantum stochastic dynamics on the predual space of a W*-algebra is presented as a noncommutative version of the Zakai equation driven by the modular quantum white noise. This is done by the noncommutative analog of the Girsanov transformation which we introduce in full QS generality.
- Files in This Item
-
Go to Link
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.