# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 42 (2013) pp.269-291

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### 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.

MSC(Primary) 34E10 37A50, 37A30, 37H99, 60E05 random dynamical system, spectral decomposition theorem, random perturbations