Stochastic shocks in a two-sector Solow model

We study a stochastic, discrete-time, two-sector growth model á-la Solow (1956) characterized by perpetual growth. Assuming that exogenous i.i.d. shocks hit the physical production sector, we show that the capital dynamics can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a Cantor set