A partial history of the early development of continuous-time nonlinear stochastic systems theory

This article is a survey of the early development of selected areas in nonlinear continuous-time stochastic control. Key developments in optimal control and the dynamic programming principle, existence of optimal controls under complete and partial observations, nonlinear filtering, stochastic stability, the stochastic maximum principle and ergodic control are discussed. Issues concerning wide bandwidth noise for stability, modeling, filtering and ergodic control are dealt with. The focus is on the earlier work, but many important topics are omitted for lack of space.