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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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