Publications of the Research Institute for Mathematical Sciences


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Volume 23, Issue 1, 1987, pp. 17–56
DOI: 10.2977/prims/1195176845

Published online: 1987-02-28

Fermion Ito's Formula II: The Gauge Process in Fermion Fock Space

David Applebaum[1]

(1) University of Nottingham, UK

The stochastic calculus constructed in [2] for fermion Brownian motion is augmented through the inclusion of stochastic integration with respect to the gauge process. The solutions of certain non-commutative stochastic differential equations are used to construct dilations of contraction semigroups on a Hilbert space ℌ0 and of uniformly continuous, completely positive semigroups on -B(ℌ0). Finally we construct a fermion analogue of the classical Poisson process and investigate some of its properties.

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Applebaum David: Fermion Ito's Formula II: The Gauge Process in Fermion Fock Space. Publ. Res. Inst. Math. Sci. 23 (1987), 17-56. doi: 10.2977/prims/1195176845