In previous work we have developed a general method for casting stochastic
partial differential equations (SPDEs) into a functional integral formalism
, and have derived the one-loop effective potential for these systems. In t
his paper we apply the same formalism to a specific field theory of conside
rable interest, the reaction-diffusion-decay system. When this field theory
is subject to white noise we can calculate the one-loop effective potentia
l (for arbitrary polynomial reaction kinetics) and show that it is one-loop
ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific c
hoices of interaction terms the one-loop renormalizability can be extended
to higher dimensions. We also show how to include the effects of fluctuatio
ns in the study of pattern formation away from equilibrium, and conclude th
at noise affects the stability of the system in a way which is calculable.