How to differentiate a quantum stochastic cocycle

Abstract

Two new approaches to the infinitesimal characterisation of quantum stochastic cocycles are reviewed. The first concerns mapping cocycles on an operator space and demonstrates the role of H\"older continuity; the second concerns contraction operator cocycles on a Hilbert space and shows how holomorphic assumptions yield cocycles enjoying an infinitesimal characterisation which goes beyond the scope of quantum stochastic differential equations.