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Quantum stochastic differential equations on *-bialgebras

Published online by Cambridge University Press:  24 October 2008

Peter Glockner
Peter Glockner
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900 Heidelberg, Germany
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Extract

Many examples of quantum independent stationary increment processes are solutions of quantum stochastic differential equations. We give a common characterization of these examples by a quantum stochastic differential equation on an abstract *-bialgebra. Specializing this abstract *-bialgebra and the coefficients of the equation, we obtain the equations for the Unitary Noncommutative Stochastic processes of [12], the Quantum Wiener Process [2], the Azéma martingales [11] and for other examples. The existence and uniqueness of a solution of the general equation is shown. Assuming the boundedness of this solution, we prove that it is a continuous and stationary independent increment process.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 3 , May 1991 , pp. 571 - 595
Copyright
Copyright © Cambridge Philosophical Society 1991

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