Noncommutative Itô and Stratonovich noise and stochastic evolutions

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