EXISTENCE OF FELLER COCYCLES ON A <i>C</i>*-ALGEBRA

Abstract

The quantum stochastic differential equation dk t = k t ∘ θ α β d Λ β α ( t ) is considered on a unital C *-algebra, with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for the existence of a completely positive contractive solution are shown to be sufficient. It is known that for completely positive contraction processes, k satisfies such an equation if and only if k is a regular Markovian cocycle. ‘Feller’ refers to an invariance condition analogous to probabilistic terminology if the algebra is thought of as a non-commutative topological space.