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Fermion Ito's formula and stochastic evolutions

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Abstract

An Ito product formula is proved for stochastic integrals against Fermion Brownian motion, and used to construct unitary processes satisfying stochastic differential equations. As in the corresponding Boson theory [10, 11] these give rise to stochastic dilations of completely positive semigroups.

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Author notes

  1. D. B. Applebaum

    Present address: Dipartimento di Matematica, II Università degli Studi di Roma, Via Orazio Raimondo, I-00173, (La Romanina) Roma, Italy

Authors and Affiliations

  1. Mathematics Department, University of Nottingham, NG7 2RD, University Park, Nottingham, England

    D. B. Applebaum & R. L. Hudson

Authors
  1. D. B. Applebaum
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  2. R. L. Hudson
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Additional information

Communicated by H. Araki

Work completed in part while the first author was supported by an SERC research studentship, and in part while the second author was visiting the Physics Department of the University of Texas at Austin supported by NSF grant PHY 81-07381

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Applebaum, D.B., Hudson, R.L. Fermion Ito's formula and stochastic evolutions. Commun.Math. Phys. 96, 473–496 (1984). https://doi.org/10.1007/BF01212531

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  • DOI: https://doi.org/10.1007/BF01212531

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