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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On some cheap control problems for diffusion processes


Authors: José-Luis Menaldi and Maurice Robin
Journal: Trans. Amer. Math. Soc. 278 (1983), 771-802
MSC: Primary 93E20; Secondary 60J60
DOI: https://doi.org/10.1090/S0002-9947-1983-0701523-2
MathSciNet review: 701523
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Abstract: We consider several cases of control problems for diffusion processes when the payoff functional does not depend explicitly on the control. We prove the continuity of the optimal cost function and give a characterization of this cost with a quasi-variational inequality interpreting the problem as limit of an impulse control problem when the cost of impulse tends to zero. Moreover, we show the existence of an optimal control for some particular situations.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0701523-2
Keywords: Optimal impulse control, diffusion processes, quasi-variational inequalities, second order elliptic operators
Article copyright: © Copyright 1983 American Mathematical Society