  We present an alternative to the perturbative diagrammatic approach for
studying stochastic dynamics. Our approach is based on an auxiliary field loop
expansion for the path integral representation for the generating functional of
the noise induced correlation functions. We derive two different effective
actions, one based on the Onsager-Machlup (OM) approach, and the other on the
Martin-Siggia-Rose (MSR) response function approach. In particular we determine
the leading order approximation for the effective action and effective
potential for arbitrary spatial dimensions for several simple systems. These
include the Kardar-Parisi-Zhang (KPZ) equation, the chemical reaction
annihilation and diffusion process $A+A \rightarrow 0$, and the Ginzburg-Landau
(GL) model for spin relaxation. We show how to obtain the effective potential
of the OM approach from the effective potential in the MSR approach. For the
KPZ equation we find that our approximation, which is non-perturbative and
obeys broken symmetry Ward identities, does not lead to the appearance of a
fluctuation induced symmetry breakdown. This contradicts the results of earlier
studies. We also obtain some of the renormalization group flows directly from
the effective potential and compare our results with exact and perturbative
results.
