The notion of quantum process with continuous trajectories is defined in terms of mutual quadratic variations and it is proved that for classical stochastic processes, this notion of continuity of trajectories coincides with the usual one. Our main result is that any continuous trajectory difference martingale M which is a Grassmann measure with scalar non-atomic brackets is isomorphic to a Fermion white noise (mean zero Fermi-Gaussian family) whose covariance coincides with the brackets of M. This is a fermion version of the Levy representation theorem for classical Brownian motion.

Accardi, L., Quaegebeur, J. (1992). A Fermion Levy theorem. JOURNAL OF FUNCTIONAL ANALYSIS, 110(1), 131-160 [10.1016/0022-1236(92)90045-K].

A Fermion Levy theorem

ACCARDI, LUIGI;
1992-01-01

Abstract

The notion of quantum process with continuous trajectories is defined in terms of mutual quadratic variations and it is proved that for classical stochastic processes, this notion of continuity of trajectories coincides with the usual one. Our main result is that any continuous trajectory difference martingale M which is a Grassmann measure with scalar non-atomic brackets is isomorphic to a Fermion white noise (mean zero Fermi-Gaussian family) whose covariance coincides with the brackets of M. This is a fermion version of the Levy representation theorem for classical Brownian motion.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - Probabilita' e Statistica Matematica
English
Accardi, L., Quaegebeur, J. (1992). A Fermion Levy theorem. JOURNAL OF FUNCTIONAL ANALYSIS, 110(1), 131-160 [10.1016/0022-1236(92)90045-K].
Accardi, L; Quaegebeur, J
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/74928
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