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 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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