Effects of multiplicative noise on fluctuation-induced transport

We study the transport of a Brownian particle moving in a ratchet-like periodic potential driven by multiplicative colored noise, and an analytic expression for the steady current with weak noise-strength is obtained. The results show that the effect of the multiplicative noise is equivalent to additive noise acting on a particle moving in an effective potential with a slope modified from the original one. Then a net steady current may arise even in the cases of white noise and a symmetric periodic potential, Some simple models are studied and discussed.