Extension of the Class of Markov Models

Arkin, V.I. (1984). Extension of the Class of Markov Models. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-84-008

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Abstract

In a recent book, the author proposed a new method of solving stochastic control problems, which, unlike the traditional approach, is not based on dynamic programming techniques. The main features of the new method are the extension of the Markov controls and the use of non-Markov controls which depend on the complete history of the process.

In this extended control domain the optimal control problem becomes a mathematical programming problem in the space of functions and can be studied using convex analysis. The author first generalizes the Markov control extension theorem for problems with constraints which depend on future time, and then obtains a method for finding the optimal control in convex problems through the solution of the auxiliary mathematical programming problem.

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