Quantumq-white noise and aq-central limit theorem |
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Authors: | Michael Schürman |
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Institution: | (1) Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, W-6900 Heidelberg, Federal Republic of Germany |
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Abstract: | We establish a connection between the Azéma martingales and certain quantum stochastic processes with increments satisfyingq-commutation relations. This leads to a theory ofq-white noise onq-*-bialgebras and to a generalization of the Fock space representation theorem for white noise on *-bialgebras. In particular, quantum Azéma noise,q-interpolations between Fermion and Boson quantum Brownian motion and unitary evolutions withq-independent multiplicative increments are studied. It follows from our results that the Azéma martingales and theq-interpolations are central limits of sums ofq-independent, identically distributed quantum random variables. |
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