The main purpose of this chapter is to study stochastic calculus for the Cvalued Markovian solution process {x s , s ∈ [t, T]} for the SHDE (1.27) and the M-valued Markovian solution process {(S(s), S s ), s ≥ 0} for the SHDE (1.43). In particular, Dynkin’s formulas, which play an important role in the Hamilton-Jacobi-Bellman theory of the optimal control problems, will be derived for these two solution processes.


Banach Space Optimal Control Problem Bounded Linear Operator Stochastic Calculus Martingale Problem 
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© Springer Science+Business Media, LLC 2008

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