JournalsprimsVol. 23, No. 1pp. 17–56

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
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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.

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. 17–56

DOI 10.2977/PRIMS/1195176845