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On time-inhomogeneous controlled diffusion processes in domains. (English) Zbl 1127.93062

Summary: The first part of this article is devoted to quite an old subject in the theory of controlled diffusion processes, namely deriving Bellman’s principle (also called the principle of optimality) for processes controlled up to the first exit time from bounded domains.
Our main results depend heavily on the validity of Bellman’s principle. Later on, these results are used to obtain sharp results concerning when the value functions for time-homogeneous processes satisfy the corresponding Bellman’s equations.

MSC:

93E20 Optimal stochastic control
90C40 Markov and semi-Markov decision processes
49L20 Dynamic programming in optimal control and differential games

References:

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