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This research monograph develops the Hamilton-Jacobi-Bellman theory via dynamic programming principle for a class of optimal control problems for stochastic hereditary differential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an infinite but fading memory. These equations represent a class of stochastic infinite-dimensional systems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering and economics/finance. This monograph covers a very active research area. It can be used as a research reference for researchers and advanced graduate students who have special interest in optimal control theory and applications of stochastic hereditary systems.
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