Titlebook: Numerical Methods for Stochastic Control Problems in Continuous Time; Harold J. Kushner,Paul G. Dupuis Book 19921st edition Springer-Verla

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The Viscosity Solution Approach to Proving Convergence of Numerical Schemes,imal control problems. The approach to proving the convergence has been based on demonstrating the convergence of a sequence of controlled Markov chains to a controlled process (diffusion, jump diffusion, etc.) appropriate to the given stochastic or deterministic optimal control problem.

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Springer-Verlag New York, Inc. 1992

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Stochastic Modelling and Applied Probabilityhttp://image.papertrans.cn/n/image/669094.jpg

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https://doi.org/10.1007/978-1-4684-0441-8Markov chain; Variation; algorithms; numerical analysis; stochastic processes

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Problems from the Calculus of Variations,A large class of deterministic optimal control problems are special cases of the stochastic optimal control problems considered previously. This is true both with respect to the construction of schemes as well as the proofs of convergence. In fact, the convergence proofs become much simpler in the deterministic setting.

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Controlled Markov Chains,ase, where there is no control or where the control is fixed, is dealt with in Section 2.1, and the recursive equations satisfied by the cost functionals are obtained. A similar method is used to get the recursive equations for the optimal value functions for the controlled problems. The optimal sto