Random perturbations of non-singular transformations on \([0,1]\) (Q354028)

The authors study random perturbations of a non-singular measurable transformation \(S:[0,1] \rightarrow [0,1]\). They obtain the existence of invariant densities for random perturbations of \(S\) using the spectral decomposition theorem of \textit{J. Komorník} and \textit{A. Lasota} [Bull. Pol. Acad. Sci., Math. 35, No. 1--10, 321--327 (1987; Zbl 0642.47026)]. Furthermore, the authors show that the densities for random perturbations with small noise converge strongly to the density for the Perron-Frobenius operator corresponding to \(S\) with respect to the \(L^1([0,1])\)-norm. This parallels a result of \textit{A. Lasota} and \textit{M. C. Mackey} [Chaos, fractals, and noise: Stochastic aspects of dynamics. 2nd ed. New York, NY: Springer-Verlag (1994; Zbl 0784.58005)].