Pub. Date:
Springer New York
Stochastic Approximation and Recursive Algorithms and Applications / Edition 2

Stochastic Approximation and Recursive Algorithms and Applications / Edition 2

by Harold Kushner, G. George YinHarold Kushner
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This revised and expanded second edition presents a thorough development of the modern theory of shastic approximation or recursive shastic algorithms for both constrained and unconstrained problems. There is a complete development of both probability one and weak convergence methods for very general noise processes. The proofs of convergence use the ODE method, the most powerful to date. 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. Rate of convergence, iterate averaging, high-dimensional problems, stability-ODE methods, two time scale, asynchronous and decentralized algorithms, state-dependent noise, stability methods for correlated noise, perturbed test function methods, and large deviations methods are covered. Many motivating examples from learning theory, ergodic cost problems for discrete event systems, wireless communications, adaptive control, signal processing, and elsewhere illustrate the applications of the theory.

Product Details

ISBN-13: 9781441918475
Publisher: Springer New York
Publication date: 11/24/2010
Series: Stochastic Modelling and Applied Probability , #35
Edition description: Softcover reprint of hardcover 2nd ed. 2003
Pages: 478
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

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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