Renormalized perturbation theory for a multiplicative noise system

We study an anharmonic overdamped oscillator driven by both additive and multiplicative Gaussian white noise. Within the Martin-Siggia-Rose formalism we employ renormalized perturbation theory to calculate the stationary correlation function and the response function of the oscillator variable. Due to the absence of a simple fluctuation-dissipation theorem renormalization cannot make use of exact stationary moments, but is perormed with the help of renormalization conditions.