Absolutely continuous invariant measures for random maps of the interval

During the talk I will discuss results on the existence of the absolutely continuous invariant measures for random maps of the interval, together with the properties of the corresponding Frobenius-Perron operator. I will present the proof of the theorem by S. Pelikan, which extends Lasota-Yorke theorem to the setting of random piecewise C^2 and monotone transformations of the interval.