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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.

Keywords

Banach Space Optimal Control Problem Bounded Linear Operator Stochastic Calculus Martingale Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2008

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