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.
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(2008). Stochastic Calculus. In: Chang, MH. (eds) Stochastic Control of Hereditary Systems and Applications. Stochastic Modelling and Applied Probability, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75816-9_3
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DOI: https://doi.org/10.1007/978-0-387-75816-9_3
Publisher Name: Springer, New York, NY
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