Towards characterizing quantum stochastic fermionic evolutions

The generalization to the case of Z2-graded von Neumann algebras of evolutions satisfying a quantum stochastic differential equation with bounded coefficients and driven by fermionic noise is presented. It is proved that the correspondence between fermionic evolutions and stochastic cocycles in this case is parallel to the one in the boson case [11]. Use of the unification technique [14] allows us to benefit from working in the boson Fock space.