عنوان

Stochastic approximation and its applications

0306481669

9780306481666

b550437

Stochastic approximation and its applications

[Book]

by Han-Fu Chen.

New York

Kluwer Academic Publishers

©2003.

(xv, 357 pages) : illustrations

Nonconvex optimization and its applications, v. 64.

Robbins-Monro algorithm. Finding zeros of a function ; Probabilistic method ; ODE method ; Truncated RM algorithm and TS method ; Weak convergence method --;Stochastic approximation algorithms with expanding truncations. Motivation ; General convergence theorems by TS method ; Convergence under state-independent conditions ; Necessity of noise condition ; Non-additive noise ; Connection between trajectory convergence and property of limit points ; Robustness of stochastic approximation algorithms ; Dynamic stochastic approximation --;Asymptotic properties of stochastic approximation algorithms. Convergence rate: nondegenerate case ; Convergence rate: degenerate case ; Asymptotic normality ; Asymptotic efficiency --;Optimization by stochastic approximation. Kiefer-Wolfowitz algorithm with randomized differences ; Asymptotic properties of KW algorithm ; Global optimization ; Asymptotic behavior of global optimization algorithm ; Application to model reduction --;Application to signal processing. Recursive blind identification ; Principal component analysis ; Recursive blind identification by PCA ; Constrained adaptive filtering ; Adaptive filtering by sign algorithms ; Asynchronous stochastic approximation --;Application to systems and control. Application to identification and adaptive control ; Application to adaptive stabilization ; Application to pole assignment for systems with unknown coefficients ; Application to adaptive regulation --;Appendices. Probability space ; Random variable and distribution function ; Expectation ; Convergence theorems and inequalities ; Conditional expectation ; Independence ; Ergodicity ; Convergence theorems for Martingale ; Convergence theorems for MDS I ; Borel-Cantelli-Levy Lemma ; Convergence criteria for adapted sequences ; Convergence theorems for MDS II ; Weighted sum of MDS --;References.

Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application.

Approximation stochastique.

MATHEMATICS -- Probability & Statistics -- General.

Stochastic approximation.

by Han-Fu Chen.

Hanfu Chen

[Book]

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