Time-average control of martingale problems: A linear programming formulation. (English) Zbl 0699.49019

Stockbridge, Richard H.

Ann. Probab. 18, No. 1, 206-217 (1990).

Summary: This paper studies the average cost for controlled systems given as solutions of the martingale problem for their generator. The control problem is reformulated as a linear programming problem and conditions are given for the existence of an optimal solution. It is further shown that the optimal control can be taken to depend only on the history of the system and that this cost remains optimal for systems with different initial distributions.

MSC:

49J55	Existence of optimal solutions to problems involving randomness
93E20	Optimal stochastic control
90C90	Applications of mathematical programming
90C05	Linear programming

Keywords:

average cost; controlled systems; martingale problem