On the spectral properties of a Markov model for learning processes

We study the spectral properties of the evolution operator of densities of the one-dimensional version of a Markov model for instrumental conditioning proposed by Bush and Mosteller in the early '50s. The model is a probabili stic combination of dynamical systems with phase space dependent probabilit y distribution. The spectral properties are derived by restricting the stoc hastic operator in the space of analytic functions. The nonergodic properti es of the model are demonstrated by the spectrum of the stochastic operator .