Pseudo-orbits, stationary measures and metastability

We characterize absolutely continuous stationary measures (acsms) of randomly perturbed dynamical systems in terms of pseudo-orbits linking the ergodic components of absolutely continuous invariant measures (acims) of the unperturbed system. We focus on those components, called least elements, which attract pseudo-orbits. Under the assumption that the transfer operators of both systems, the random and the unperturbed, satisfy a uniform Lasota-Yorke inequality on a suitable Banach space, we show that each least element is in a one-to-one correspondence with an ergodic acsm of the random system.