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Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty

We study a one-sector stochastic optimal growth model, where the utility function is iso-elastic and the production function is of the Cobb–Douglas form. Production is affected by a multiplicative shock taking one of two values. We provide sufficient conditions on the parameters of the model under which the invariant distribution of the stochastic process of optimal output levels is of the Cantor type.