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Stochastic processes with independent increments on a group are generalized to the concept of "white noise" on a Hopf algebra or bialgebra. The main purpose of the book is the characterization of these processes as solutions of quantum stochastic differential equations in the sense of R.L. Hudson and K.R. Parthasarathy. The notes are a contribution to quantum probability but they are also related to classical probability, quantum groups, and operator algebras. The Az ma martingales appear as examples of white noise on a Hopf algebra which is a deformation of the Heisenberg group. The book should be of interest to probabilists and quantum probabilists. Specialists in algebraic structures who are curious about the role of their concepts in probablility theory as well as quantum theory may find the book interesting. The reader should have some knowledge of functional analysis, operator algebras, and probability theory.
Del 18 - Qp-pq: Quantum Probability And White Noise Analysis
Quantum Probability And Infinite Dimensional Analysis: From Foundations To Appllications
Inbunden, Engelska, 2005
3 187 kr
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This volume collects research papers in quantum probability and related fields and reflects the recent developments in quantum probability ranging from the foundations to its applications.
Del 20 - Qp-pq: Quantum Probability And White Noise Analysis
Quantum Probability And Infinite Dimensional Analysis - Proceedings Of The 26th Conference
Inbunden, Engelska, 2007
2 352 kr
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This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability, 'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity illustrates that research in quantum probability and infinite dimensional analysis is very active and strongly involved in modern mathematical developments and applications.