Controlled diffusion processes. (English) Zbl 1189.93143

Borkar, Vivek S.

Probab. Surv. 2, 213-244 (2005).

Summary: This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched.

MSC:

93E20	Optimal stochastic control
49L20	Dynamic programming in optimal control and differential games
60H30	Applications of stochastic analysis (to PDEs, etc.)
60J60	Diffusion processes

Keywords:

controlled diffusions; optimal control; dynamic programming; Hamilton-Jacobi-Bellman equations; partial observations