Open Access
2005 Controlled diffusion processes
Vivek S. Borkar
Probab. Surveys 2: 213-244 (2005). DOI: 10.1214/154957805100000131


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.


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Vivek S. Borkar. "Controlled diffusion processes." Probab. Surveys 2 213 - 244, 2005.


Published: 2005
First available in Project Euclid: 19 September 2005

zbMATH: 1189.93143
MathSciNet: MR2178045
Digital Object Identifier: 10.1214/154957805100000131

Primary: 93E20
Secondary: 60H30

Keywords: controlled diffusions , dynamic programming , Hamilton-Jacobi-Bellman equations , optimal control , partial observations

Rights: Copyright © 2005 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.2 • 2005
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