Functional integral methods for stochastic fields

We study a method proposed recently that gives a unified view of the properties of stochastic fields determined by Langevin-type equations. The functional integrals involved are shown to need an additional prescription to be defined, this prescription being related to the relative order of noncommuting operators in the corresponding operator formalism which we characterize in detail. It is proved that the prescription is responsible for an additional term which has given rise to difficulties of interpretation in the Onsager-Machlup path probability density. We prove that all results are independent of this term. In particular in perturbation theory the cancellation mechanism of the prescription dependence is studied in detail.