Stochastic Approximation and Recursive Algorithms and Applications

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ISBN-13:
9780387008943
Erscheinungsdatum:
01.07.2003
Seiten:
478
Autor:
Harold Kushner
Gewicht:
834 g
Format:
241x162x30 mm
Serie:
35, Stochastic Modelling and Appli
Sprache:
Englisch
Beschreibung:

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
The book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both
constrained and unconstrained problems. The assumptions and proof
methods are designed to cover the needs of recent applications. The
development proceeds from simple to complex problems, allowing the
underlying ideas to be more easily understood. Many examples
illustrate the application of the theory.
This second edition is a thorough revision, although the main features
and the structure remain unchanged. It contains many additional
applications and results, and more detailed discussion.
Introduction
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
8.1 Motivating Examples
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