Adiabatic elimination in stochastic systems. I. Formulation of methods and application to few-variable systems

Adiabatic elimination of stochastic variables is formulated in a systematic and largely rigorous manner, and applied to a variety of examples. Ambiguities in naive methods are resolved, and it is shown that the resultant stochastic differential equation is not always to be interpreted as an Ito or as a Stratonovich stochastic differential equation. A class of nonlinear examples is also treated in which naive methods fail completely.