Second order necessary conditions of optimality for stochastic systems with variable delay
Author:
Ch. A. Agayeva
Journal:
Theor. Probability and Math. Statist. 83 (2011), 1-12
MSC (2010):
Primary 93E20, 49K45
DOI:
https://doi.org/10.1090/S0094-9000-2012-00837-5
Published electronically:
February 2, 2012
MathSciNet review:
2768844
Full-text PDF Free Access
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Abstract: The purpose of this paper is to give necessary conditions of optimality of nonlinear stochastic control systems with variable delay for singular controls. As a result, the second order necessary optimality condition for the stochastic system with uncontrolled diffusion coefficient is obtained.
References
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References
- V. B. Kolmanovskiĭ and A. D. Myshkis, Applied Theory of Functional-Differential Equations, Kluwer Academic Publishers, Dordrecht, 1992. MR 1256486 (95f:34092)
- E. F. Tsar’kov, Random Perturbations of Functional-Differential Equations, Riga, 1989. (Russian) MR 1036733 (90m:34164)
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- Ch. A. Agayeva and J. J. Allahverdiyeva, Maximum principle for stochastic systems with variable delay, Reports of NSA of Azerbaijan LIX (2003), 61–65. (Russian) MR 2186880
- Ch. A. Agayeva, Stochastic optimal control problem with delay, Theory of Stochastic Processes (2006), no. 1–2, 3–11. MR 2316281 (2007m:93092)
- I. Ekeland, Nonconvex minimization problem, Bull. Amer. Math. Soc. (NS) (1979), no. 1, 443–474. MR 526967 (80h:49007)
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Additional Information
Ch. A. Agayeva
Affiliation:
Yasar University, Izmir, Turkey, and Institute of Cybernetics, Baku, Azerbaijan
Email:
cher.agayeva@rambler.ru, agaeva.cherkez@yasar.edu.tr
Keywords:
Stochastic differential equations with delay,
stochastic control problem,
necessary condition of optimality,
singular controls,
adjoint stochastic differential equations
Received by editor(s):
December 25, 2007
Published electronically:
February 2, 2012
Article copyright:
© Copyright 2012
American Mathematical Society