Titlebook: Numerical Methods for Stochastic Control Problems in Continuous Time; Harold J. Kushner,Paul Dupuis Textbook 2001Latest edition Springer S

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Convergence for Reflecting Boundaries, Singular Control and Ergodic Cost Problems,ergence of the rescaled processes and characterizing the limits, the rescaling is inverted to obtain the desired results. This “inversion” is possible due to the conditions imposed on the allowable reflection directions. The time rescaling idea appears to be a rather powerful tool.

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Problems from the Calculus of Variations: Infinite Time Horizon,ing cost is incurred. The problem of control until the domain is exited (without the possibility of controlled stopping) can be obtained as a special case, simply by choosing a stopping cost that is sufficiently large.

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Construction of the Approximating Markov Chain,dures are clear, the reader can adapt them to particular problems which might not be directly covered by the discussion. The development does not directly cover processes on manifolds such as the surface of a sphere or torus, but the various possibilities should be apparent.

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The Ergodic Cost Problem: Formulation and Algorithms,olled diffusion (5.3.1) or jump diffusion (5.6.1). The approximating Markov chains {.., . < . } will be locally consistent with these processes. As in the previous chapters, .. denotes the state space, and ∂ .. ⊂ .. the set of reflecting states. Recall that the reflection is instantaneous and that we use ..(.,.) = 0 for . ∈ ∂ ...

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Textbook 2001Latest editionfusion term and the jump distribution can be controlled. Also, a great deal of new material concerning deterministic problems has been added, including very efficient algorithms for a class of problems of wide current interest. This book is concerned with numerical methods for stochastic control and

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Heavy Traffic and Singular Control Problems: Examples and Markov Chain Approximations,, we need to be sure that optimal or nearly optimal controls (and the minimum value function, respectively) for the aggregated problem will also be nearly optimal for the actual physical problem (and a good approximation to the associated minimum value function, respectively).

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Harold J. Kushner,Paul DupuisThe book is completely self-contained and accessible to all .Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoreti