Quantum white noise analysis and quantum stochastic equations
- Title
- Quantum white noise analysis and quantum stochastic equations
- Other Titles
- Quantum Probability and Related Topics
- Author
- 허재성
- Keywords
- Quantum Ito algebra; White Noise Analysis; Girsanov Transformation; Stochastic Master Equations
- Issue Date
- 2011-01
- Publisher
- Singapore; World Scientific
- Citation
- PQ QP, 2011, 27, P.90-124
- Abstract
- We review the basic concepts of quantum stochastic analysis using the universal Ito B*-algebra approach. The thermal quantum white noise as a noncommutative analog of the Levy-Ito process is characterized in terms of the modular B*-Ito 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.Read More: https://www.worldscientific.com/doi/abs/10.1142/9789814338745_0005
- URI
- https://www.worldscientific.com/doi/abs/10.1142/9789814338745_0005http://hdl.handle.net/20.500.11754/52959
- DOI
- 10.1142/9789814338745_0005
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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