Non-commutative Ito and Stratonovich noise and stochastic evolutions

We complete the theory of non-commutative stochastic calculus by introducing the Stratonovich representation. The key idea is to develope a theory of white noise analysis, for both the Ito and Stratonovich representations, which is based on distributions over piecewise continuous functions mapping into a Hilbert space. As an example, we give a derive the most general class of unitary stochastic evolutions, when the Hilbert space is the space of complex numbers, by first constructing the evolution in the Stratonovich representation where unitarity is self-evident.