White-noise limit of nonwhite nonequilibrium processes

The asymptotic behavior of a stochastic process subject to a colored noise is considered in the limit of vanishing correlation time of the noise. The interpretation of the multiplicative noise of the effective equation is investigated. The mathematically consistent formulation of the stochastic calculus for the limiting process is given. It differs in general from the Stratonovich one which is recovered when the colored noise obeys detailed balance or is a one-dimensional process.