Stochastic approximation and recursive algorithms and applications
Author(s)
Bibliographic Information
Stochastic approximation and recursive algorithms and applications
(Applications of mathematics, 35)
Springer, c2010
2nd ed.
- : pbk.
Available at 1 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. [443]-463) and indexes
Description and Table of Contents
Description
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.
Table of Contents
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
&nb
by "Nielsen BookData"