In the paper, a one-sector neoclassical model with stochastic growth has been constructed. The key concept of economic maturity is well-defined in the abstract model economy, and also a thorough characterization of the minimum time needed to economic maturity is supplied for the first time....

Stationary and ergodic probability distribution is derived and the stochastic balanced path of capital accumulation is defined via corresponding martingale path. Moreover, stochastic version of asymptotic turnpike theorem is established in the sense of uniform topology and also neighborhood type...