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Stochastic Approximation and Recursive Algorithms and Applications

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ISBN-10: 0387008942

ISBN-13: 9780387008943

Edition: 2nd 2003 (Revised)

Authors: Harold J. Kushner, G. George Yin

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The book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic 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, with which the asymptotic behavior is characterized by the limit behavior of a mean ODE. 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…    
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Book details

Edition: 2nd
Copyright year: 2003
Publisher: Springer
Publication date: 7/17/2003
Binding: Hardcover
Pages: 478
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.848
Language: English

Review of Continuous Time Models
Martingales and Martingale Inequalities
Stochastic Integration
Stochastic Differential Equations: Diffusions
Reflected Diffusions
Processes with Jumps
Controlled Markov Chains
Recursive Equations for the Cost
Optimal Stopping Problems
Discounted Cost
Control to a Target Set and Contraction Mappings
Finite Time Control Problems
Dynamic Programming Equations
Functionals of Uncontrolled Processes
The Optimal Stopping Problem
Control Until a Target Set Is Reached
A Discounted Problem with a Target Set and Reflection
Average Cost Per Unit Time
Markov Chain Approximation Method: Introduction
Markov Chain Approximation
Continuous Time Interpolation
A Markov Chain Interpolation
A Random Walk Approximation
A Deterministic Discounted Problem
Deterministic Relaxed Controls
Construction of the Approximating Markov Chains
One Dimensional Examples
Numerical Simplifications
The General Finite Difference Method
A Direct Construction
Variable Grids
Jump Diffusion Processes
Reflecting Boundaries
Dynamic Programming Equations
Controlled and State Dependent Variance
Computational Methods for Controlled Markov Chains
The Problem Formulation
Classical Iterative Methods
Error Bounds
Accelerated Jacobi and Gauss-Seidel Methods
Domain Decomposition
Coarse Grid-Fine Grid Solutions
A Multigrid Method
Linear Programming
The Ergodic Cost Problem: Formulation and Algorithms
Formulation of the Control Problem
A Jacobi Type Iteration
Approximation in Policy Space
Numerical Methods
The Control Problem
The Interpolated Process
Boundary Costs and Controls
Heavy Traffic and Singular Control
Motivating Examples
The Heavy Traffic Problem
Singular Control
Weak Convergence and the Characterization of Processes