RANDOM PERTURBATIONS OF NON-SINGULAR TRANSFORMATIONS ON [0; 1]

Abstract. We consider random perturbations of non-singular measur-able transformations S on [0; 1]. By using the spectral decomposition theorem of Komornik and Lasota, we prove that the existence of the invariant densities for random perturbations of S. Moreover the densi-ties 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