Stochastic growth with a likelihood-increasing estimation process

We formulate an optimal estimation process in a stochastic growth model with an unknown true probability model. We consider a general reduced model of capital accumulation with an infinite horizon and introduce a learning process in the stochastic dynamic programming. When the only available information is a sample realization generated by a stationary and ergodic stochastic process, we prove that the optimal estimation process based on likelihood-increasing behavior converges to the true probability measure and the likelihood-increasing estimator defines a transition function on the sample space. Copyright Springer-Verlag Berlin/Heidelberg 2006