This paper explores the formulation and analysis of linear equilibrium models of investment in which learning is perpetual and informationally decentralized firms need never share the same beliefs concerning time series relevant to their decisions. Recursive, Kalman filtering techniques are shown to be applicable in an illustrative, hierarchical information structure, and a nonlinear technique of undetermined coefficients is shown to be applicable in an illustrative, symmetric information structure in which there is a confounding of laws of motion with forecasting problems. The equilibrium time series of these models can display interesting movement in response to shocks and measurement errors, including persistence, certain cross-correlation properties, and damped oscillations. That is, forecasts errors are serially correlated over decision makers and serially correlated over time in a certain crucial sense. More generally, these models do place restrictions on observed time series and can be fitted to data.