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.
Cite this article
David Applebaum, Fermion Ito's Formula II: The Gauge Process in Fermion Fock Space. Publ. Res. Inst. Math. Sci. 23 (1987), no. 1, pp. 17–56DOI 10.2977/PRIMS/1195176845