Asymptotic stochastic transformations for nonlinear quantum dynamical systems

The Ito and Stratonovich approaches are carried over to quantum stochastic systems. Here the white noise representation is shown to be the most approp riate as here the two approaches appear as Wick and Weyl orderings, respect ively. This introduces for the first time the Stratonovich form for SDEs dr iven by Poisson processes or quantum SDEs including the conservation proces s. The relation of the nonlinear Heisenberg ODEs to asymptotic quantum SDEs is established extending previous work on linear (Schrodinger) equations. This is shown to generalize the classical integral transformations between the various forms of stochastic calculi and to extend the Khasminskii theor em to the quantum setting.