Later, the rigorous theoretical analysis needed to support normal form coordinate transforms was developed in Refs. 23 and 24. The technical problem of the anticipative noise integrals also was dealt with rigorously in this work. Even later, another stochastic normal form transformation was developed. 25 This new method allows for the "͓removal of͔ anticipation… from the slow modes with the result that no anticipation is required after the fast transients decay" ͑Ref. 25, p. 13͒. The removal of anticipation leads to a simplification of the normal form. Nonetheless, this simpler normal form retains its accuracy with the original stochastic system. 25 We shall use the method of Ref. 25 to simplify our stochastic dynamical system to one that emulates the long-term dynamics of the original system. The method involves five principles, which we recapitulate here for completeness: