000 | 00404nam a2200145Ia 4500 | ||
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999 |
_c170299 _d170299 |
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020 | _a0387008942 | ||
040 | _cCUS | ||
082 |
_a519.22 _bKUS/S |
||
100 | _aKushner, Harold J. | ||
245 | 0 |
_aStochastic approximation and recursive algorithms and applications/ _cHarold J. Kushner and G. George Yin |
|
250 | _a2nd ed. | ||
260 |
_aNew York: _bSpringer, _c2003. |
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300 |
_axxii, 474 p. ; _c25 cm. |
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440 |
_a(Applications of Mathematics), _v35 |
||
505 | _aIntroduction 1 Review of Continuous Time Models 1.1 Martingales and Martingale Inequalities 1.2 Stochastic Integration 1.3 Stochastic Differential Equations: Diffusions 1.4 Reflected Diffusions 1.5 Processes with Jumps 2 Controlled Markov Chains 2.1 Recursive Equations for the Cost 2.2 Optimal Stopping Problems 2.3 Discounted Cost 2.4 Control to a Target Set and Contraction Mappings 2.5 Finite Time Control Problems 3 Dynamic Programming Equations 3.1 Functionals of Uncontrolled Processes 3.2 The Optimal Stopping Problem 3.3 Control Until a Target Set Is Reached 3.4 A Discounted Problem with a Target Set and Reflection 3.5 Average Cost Per Unit Time 4 Markov Chain Approximation Method: Introduction 4.1 Markov Chain Approximation 4.2 Continuous Time Interpolation 4.3 A Markov Chain Interpolation 4.4 A Random Walk Approximation 4.5 A Deterministic Discounted Problem 4.6 Deterministic Relaxed Controls 5 Construction of the Approximating Markov Chains 5.1 One Dimensional Examples 5.2 Numerical Simplifications 5.3 The General Finite Difference Method 5.4 A Direct Construction 5.5 Variable Grids 5.6 Jump Diffusion Processes 5.7 Reflecting Boundaries 5.8 Dynamic Programming Equations 5.9 Controlled and State Dependent Variance 6 Computational Methods for Controlled Markov Chains 6.1 The Problem Formulation 6.2 Classical Iterative Methods 6.3 Error Bounds 6.4 Accelerated Jacobi and Gauss-Seidel Methods 6.5 Domain Decomposition 6.6 Coarse Grid-Fine Grid Solutions 6.7 A Multigrid Method 6.8 Linear Programming 7 The Ergodic Cost Problem: Formulation and Algorithms 7.1 Formulation of the Control Problem 7.2 A Jacobi Type Iteration 7.3 Approximation in Policy Space 7.4 Numerical Methods 7.5 The Control Problem 7.6 The Interpolated Process 7.7 Computations 7.8 Boundary Costs and Controls 8 Heavy Traffic and Singular Control | ||
650 | _aRecursive functions | ||
650 | _aStochastic approximation | ||
650 | _aAlgorithms | ||
700 | _aYin, G. George | ||
942 | _cWB16 |