Publications of the Research Institute for Mathematical Sciences
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Published online: 1987-02-28
Fermion Ito's Formula II: The Gauge Process in Fermion Fock SpaceDavid Applebaum (1) University of Nottingham, UK
The stochastic calculus constructed in  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