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A Lévy theorem for free noises. (English) Zbl 0729.60074

We prove a Lévy type characterization theorem for the free Brownian motion and the free Poisson process using martingale and covariance conditions and some assumption on fourth order conditional moments.
Reviewer: F.Fagnola (Povo)

MSC:

60J65 Brownian motion
60G44 Martingales with continuous parameter
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[1] Accardi, L.; Parthasarathy, K. R., A Martinagle characterization of canonical commutation and anticommutation relations, J. Funct. Anal., 77, 211-231 (1988) · Zbl 0642.60032
[2] Accardi, L., Quaegebeur, J.: A Fermion Lévy theorem. J. Funct. Anal. (to appear) · Zbl 0770.60050
[3] Accardi, L., Fagnola, F., Quaegebeur, J.: A representation free quantum stochastic calculus. Centro Matematico V. Volterra. Rome. J. Funct. Anal. (to appear) · Zbl 0759.60068
[4] Fagnola, F., A martingale characterization of quantum Poisson processes, Probab. Theory. Relat. Fields, 84, 323-333 (1990) · Zbl 0694.60045
[5] Glockner, P., Schürmann, M., Speicher, R.: Realization of free white noises. SFB-preprint 564. Heidelberg, 1990 · Zbl 0724.60104
[6] Letta, G., Martingales et intégration stochastique. Scuola normale superiore, quaderni (1984), Pisa Bologna: Monograf, Pisa Bologna · Zbl 0569.60053
[7] Parthasarathy, K.R., Sinha, K.B.: Unification of quantum noise processes in Fock spaces. Proceedings, Trento 1990, Quantum Probab. Appl. (to appear) · Zbl 0942.46047
[8] Speicher, R., A new example of “independence” and “white noise”, Probab. Theory. Relat. Fields, 84, 141-159 (1990) · Zbl 0671.60109
[9] Voiculescu, D.; Araki, H.; Moore, C. C.; Stratila, S.; Voiculescu, D., Symmetries of some reduced free productC^*-algebras, Operator algebras and their connection with topology and ergodic theory, 556-588 (1985), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0618.46048
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