Random perturbations of non-singular transformations on [0,1]

Abstract

We consider random perturbations of non-singular measurable transformations S on [0,1]. By using the spectral decomposition theorem of Komorník and Lasota, we prove that the existence of the invariant densities for random perturbations of S. Moreover the densities for random perturbations with small noise strongly converges to the deinsity for Perron-Frobenius operator corresponding to S with respect to L¹([0,1])-norm.