JournalsprimsVol. 23 , No. 1DOI 10.2977/prims/1195176845

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

  • David Applebaum

    University of Nottingham, UK
Fermion Ito's Formula II: The Gauge Process in Fermion Fock Space cover

Abstract

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.