Discrete Approximations of Controlled Stochastic Systems with Memory: A Survey |
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Authors: | Mou-Hsiung Chang |
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Institution: | 1. Mathematical Sciences Division , U.S. Army Research Office , Research Triangle Park , North Carolina , USA mouhsiung.chang.civ@mail.mil |
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Abstract: | This survey article considers discrete approximations of an optimal control problem in which the controlled state equation is described by a general class of stochastic functional differential equations with a bounded memory. Specifically, three different approximation methods, namely (i) semidiscretization scheme; (ii) Markov chain approximation; and (iii) finite difference approximation, are investigated. The convergence results as well as error estimates are established for each of the approximation methods. |
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Keywords: | Discrete approximations Finite difference approximation Markov chain approximation Stochastic functional differential equations |
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